+ All Categories
Home > Documents > Methods for Estimating a Conditional Distribution Function ...

Methods for Estimating a Conditional Distribution Function ...

Date post: 19-Oct-2021
Category:
Upload: others
View: 8 times
Download: 0 times
Share this document with a friend
24
Peter Hall, Rodney C. L. Wolff and Qiwei Yao Methods for estimating a conditional distribution function Article (Accepted version) (Refereed) Original citation: Hall, Peter and Wolff, Rodney C. L. and Yao, Qiwei (1999) Methods for estimating a conditional distribution function. Journal of the American Statistical Association , 94 (445). pp. 154-163. Stable URL: http://www.jstor.org/stable/2669691 © 1999 American Statistical Association This version available at: http://eprints.lse.ac.uk/6631/ Available in LSE Research Online: February 2009 LSE has developed LSE Research Online so that users may access research output of the School. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LSE Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. You may freely distribute the URL (http://eprints.lse.ac.uk) of the LSE Research Online website. This document is the author’s final manuscript accepted version of the journal article, incorporating any revisions agreed during the peer review process. Some differences between this version and the published version may remain. You are advised to consult the publisher’s version if you wish to cite from it.
Transcript
Page 1: Methods for Estimating a Conditional Distribution Function ...

Peter Hall, Rodney C. L. Wolff and Qiwei YaoMethods for estimating a conditional distribution function Article (Accepted version) (Refereed)

Original citation: Hall, Peter and Wolff, Rodney C. L. and Yao, Qiwei (1999) Methods for estimating a conditional distribution function. Journal of the American Statistical Association, 94 (445). pp. 154-163. Stable URL: http://www.jstor.org/stable/2669691 © 1999 American Statistical Association This version available at: http://eprints.lse.ac.uk/6631/Available in LSE Research Online: February 2009 LSE has developed LSE Research Online so that users may access research output of the School. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LSE Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. You may freely distribute the URL (http://eprints.lse.ac.uk) of the LSE Research Online website. This document is the author’s final manuscript accepted version of the journal article, incorporating any revisions agreed during the peer review process. Some differences between this version and the published version may remain. You are advised to consult the publisher’s version if you wish to cite from it.

Page 2: Methods for Estimating a Conditional Distribution Function ...

������������ �������������������������� ������������ �"!#��������"��$&%'������( )%�� � �����*�

+-,�./,�02143657598 :�;=<?>@,�A�BDCFEGC@H�;I5KJ-8/L M NDOQPR,�OTSU3V;W8/L X

�ZY-[�\^]�_a`6\cbed�;6.fOQgV3V./,�<ihjAk.fl@,2m?0f;6h?5Q,�no;6prq/,�./.fO7>as�ma0t,�<aO7uv.fOQ;I>ZO7>c./,�0tg�3657qRO7>Z.fO7n*,Dq/,�0tOQ,�qR36>a365QAWqfO7q�wcPR,qfx@s6s6,�q/.).yPz;">@,�P{n,�.fl@;=<?qep|;602uv;I>a<aOQ.fOQ;I>?365}<aO7q/./[email protected];I>Z,�q/.fO7n3V.fO7;I>}CU~)l@,��?0tq/.)O7qeh�36q/,�<�;I>'5Q;Wu�36575QA�a./.fO7>@sk3Z5Q;6sIO7q/.fO�u�n*;W<@,�5�w�36>?<�O7q2O7>�.fl@,�q/m?OQ0tO7.e;6p�0f,�uv,�>c.2Pz;60t��;I> 5Q;Wu�36575QA"m?3V0t36n,�./0tO7u�./,�u�la>aO7�=x@,�q2O7><@,�>aqfOQ.yA�,�q/.fO7n3V.fO7;I>}C���.2m?0f;=<?xauv,�q�<aO�q/./0tOQh?xa.fOQ;I>i,�q/.fO7n3V./;60�q2.fl?3V.4n3^A'h�,�;6pU3V0th?OQ./0t3V0tO�5QA"l?OQsIl';60t<a,�0�wh?x@.�>@,�g6,�0t.fl@,�5Q,�qfq�365QP�3�AWq�5�OQ,h�,�.�PR,�,�>���36>a<��VC�~)l@,"q/,�uv;I>a<�n*,�.fl@;W<�O7>jg6;I5Qg6,�q�36>�36<��fxaq/./,�<�p|;60�n;6p�.fl@,��436<a3V0t3^AI3��cH�3V.fq/;I>�,�q/.fO�n3V./;60�Ce��.�ma0f,�qf,�0fg6,�q�.fla,�h?O736q236>a<'gV3V0tO736>?uv,�ma0f;6m�,�0f.fO7,�qe;6pG3ku�5736qtq�;6pq/,�uv;I>a<W��;60t<a,�0�,�q/.fO7n3V./;60tq�O7>c./0t;=<ax?uv,�< h=A'SUx�36>?<��6;I>@,�q�����6�6�I��[email protected]@,36<a<a,�<�36<@g�36>j.f3Vs6,;6p365QPR3^A=q�hT,�O�>@s�3�<aO7q/./[email protected];I> OQ.fq/,�5Qp�C* �x@0�n*,�.fl@;W<aq�3657q/;'l?3�g6,k3Vmam�57O7u�3V.fOQ;I>�;[email protected]�<@,&.fl@,*.fO7n*,q/,�0�OQ,�qq/,�./.fO7>@s@w�p|;604,v¡W36nm?5Q,�./;"�jxa36>j.fO75Q,�,�q/.fO7n3V.fOQ;I>�p|;604O7>a<@,�m�,�>a<a,�>c.e<a3V.f3WC)~)l?O7qema0f;6h�5Q,�n¢n*;6.fOQgV3V./,�<�SUx36>a<��6;I>a,�q�£@Pz;60t��C

¤�¥j¦}§�¨�]�©-[6b)ª2h?q/;I57x@./,�57Ak0f,�sIxa5�3V0�wWh?36>a<@P�O�<@.fl}w=h?O736q/,�<ih�;=;6.fq/./0t3Vm�wauv;I>a<?OQ.fOQ;I>a365}<aO�q/./0tOQh?xa.fOQ;I>}wI�6,�0t>a,�5n*,�.fl@;W<aq�wc5Q;Wu�365a57O�>@,�3V0Gn*,�.fl@;W<aq�wc57;=u�365a57;6sIO7q/.fO7uen*,�.fla;=<aq�wj�436<a3V0t3�AI3��cH�3V.fqf;I>i,�q/.fO7n3V./;60�w=ma0f,�<?O7uv.fOQ;I>}w�jxa36>j.fO75Q,�,�qf.fO7n3V.fOQ;I>}[email protected]�n*,�q/,�0tOQ,�qe36>?365QA=qtO7q�w@PR,�OQsIlc./,�<'hT;=;6.fq/./0t3Vm«C

�}¬r¨?]�\\�­|\�®¯¥�b)B�;I>a<aOQ.fOQ;I>?365T<?O7q/./0tOQh�[email protected];I>,�qf.fO7n3V.fOQ;I>

°�±T²�³�´�µ�²?¶¸·�µ@¹Dºt´�»�²�¼)ºt´�½F¾�¿@ºt³VÀÁ½Â´�¿WëÄ�Ä�ÅF½F¾/ºf´�½Æ·�³�¿�Ç�ÃrÈ�¿9´�µ�º�ÅF½Æº�³GÉÁºf´�½F·Ê³VºtÅ�Ë-³�½ÆÌʲ�µ�¿�½Â´¯Í�Çt±�ºt³^Î6²yµ�µ�º^Ç�ë±�Ï�ÐvÑtÐÊÐ�ÇvëÈ�¿9´�µ�º�ÅF½ÆºÒ�Ó ¾�»�·�·�Åv·�¶�¹Dºt´�»�²�¼)ºt´�½F¾�¿�ÇÊÔ-È�²�²�³�¿�Åƺt³VÀÁË-³�½FÌv²�µ�¿�½Â´¯Ír·�¶�Ï=²�¾�»�³�·ÊÅF·ÊÕtÍ�Ç�ÖÁ×TØkÙT·/ÚGÑfÛvÜ�Û^ÇvÙ?µ�½Æ¿�Î�º�³�²ÊÇÊÔÁÝjÞ*ÛvÐ�Ð^ß�ÇvëÈ�¿9´�µ�º�ÅF½Æºà�á ³�¿9´�½F´�È^´�²r·t¶@¹Dºf´�»�²�¼)ºf´�½F¾�¿�ºt³VÀ Ó ´�ºf´�½Æ¿9´�½F¾�¿�Ç^Ër³�½FÌv²�µ�¿�½Â´¯Í�·�¶jâ�²�³�´�ºf´�±�º�³�´�²�µ�Î�È�µ�Í�Ç^±�ºt³�´�²�µ�Î�È^µ�Í�Ç�â�²�³�´�±�Ï�ÑUãtÉ-äTÇ�Ë-â

Page 3: Methods for Estimating a Conditional Distribution Function ...

å æaç4è�é}ê�ëì&í-è�îtê2ç

��>�3�gV3V0tOQ,�.yA ;6p�q/.f3V.fO7qf.fO7u�365�ma0f;6h�5Q,�nq�w},�q/.fO�n3V.fOQ;I>ï;6p�3'uv;I>a<aOQ.fO7;I>a365Á<aO7q/./[email protected];I>�p¯xa>?uv.fOQ;I>�O7q�3i�6,�A36q/m�,�uv.4;6pzO7>@p¯,�0f,�>auv,6C�BR;I>aqfO�<@,�0�w?p¯;60D,v¡W36nm?5Q,6w�,�q/.fO7n3V.fO7;I> ;6pz.fl@,&�jxa36>j.fO75Q,�p¯x?>auv.fOQ;I> ;6pzðñsIOQg6,�>�ò�wxaqfO7>@s*3Zqf36n*m?5Q,�;6p�O7>?<@,�m�,�>a<@,�>j.�<?3V.f3*m?36OQ0tq�ój�¯ò 8^ô ð 8 � ô�õ�õ�õ�ô �¯ò*ö ô ð�öW�t÷IC�~)laO�qema0f;6h?57,�nñla36q)0f,�uv,�>j.f5QAhT,�,�>'.f36uf�W5Q,�<�h=AZSUx�36>a<��I;I>@,�q������6�6�I�)gWO7336>'O7>as6,�>aOQ;Ixaqe3Vmam�57O7u�3V.fOQ;I>i;6pÁ.fl@,*øÆ<a;Ix@h?5Q,��6,�0t>a,�5�wQ£?5Q;Wu�36557O7>@,�3V0�3Vmama0f;I36u�l";6p«ùa36>}wWSU3V;36>a<"~r;I>@s'�����6�6úI��Czªû./,�u�la>aO7�=x@,D365Q./,�0t>a3V.fO7g6,2./;&.fla3V.�;6p}SUxi36>a<��6;I>a,�qPz;Ixa5�<�h�,k./;ï,�n*m�5Q;^A�.fla,"�436<a3V0t3^AI3��cH�3V.fq/;I>ü,�qf.fO7n3V./;60�wU3657.fl@;Ix@sIl�OQ.�PR;Ixa57<�qfxWJ�,�0&.fl@,Z,v¡@uv,�qfqfO7g6,h?O736q&ma0f;6h�5Q,�nq&O7>al@,�0t,�>c.&O7>ý.fla3V.3Vmam?0f;I36utl}þ)qf,�,�p|;60,v¡@36n*m?57,'Beljxÿ36>a< d 3V0f0f;I>{�����6�W�^�*36>a<ÿùa36>�����6� � ��Cª2>a;6.fl@,�0�3Vmam?57O7u�3V.fO7;I>';6pUuv;I>a<?OQ.fOQ;I>a365r<aO7q/./[email protected];I>i,�q/.fO�n3V.fOQ;I>}wT.flaO7q2.fO7n*,&O7>jg6;I5Qg=O�>@sk<@,�m�,�>a<@,�>j.

<a3V.f3Ww�O7q'uv;I>?q/./0txauv.fOQ;I> ;6p&ma0f,�<aO7uv.fO7;I>#O7>c./,�0tg�3657q'p|;60 .fl@,�>@,v¡W.'gV3657x@,�O7> 3üq/.f3V.fOQ;I>?3V0fA .fO7n*,�q/,�0�OQ,�qó^ð 8�ô�õ�õ�õ�ô ð�öa÷ICý��p�.fl@,�.fO�n*,�q/,�0tOQ,�q*O7qd 3V0f�6;�g=O736> .fl@,�>ýPz,'nk3�Aÿq/;I5Qg6,�.fl@,ima0t,�<aO7uv.fOQ;I>�ma0f;6h�5Q,�n�hjA,�q/.fO7n3V.fO7>asZ.fl@,&<aO7qf./[email protected];I>i;6pUð���� 8 uv;I>a<aOQ.fOQ;I>?365�;I>ïð�����«w}36>a<�3Vmam?57A=O7>as.fl@,�0f,�qfxa5Q.4O7> .fl@,�u�36qf,�� ð�ö?C�d�;60f, s6,�>@,�0t36575QA6wRPR,�nOQsIlj.P�O7qtlý./;�,�q/.fO7n3V./, .fl@,�<aO�q/./0tOQh?xa.fOQ;I>�;6p�ð��� 8 sIOQg6,�> 3�qfnk36575q/,�uv.fOQ;I>�;6p�.fl@,k0f,�uv,�>c.�m?36q/.�w-qfxautl�36qZ�9ð� ô ð��� 8 � � ��� 8�ô � M ��C��R;6.fl�ma0t;6h?5Q,�nq�n3^A�h�,q/;I5Qg6,�<�xaqtO7>@sn*,�.fl@;W<aq)qfxau�l'36qe.fl@;Iqf,�qfx@s6s6,�q/./,�<�hjA"SUx'36>?<��6;I>@,�q������6�6�I��C

H l?O75Q,�5Q;Wu�365�57O7>a,�3V0�n*,�.fl@;W<aqe;6p�.fl@,�SUx�36>a<��6;I>@,�qe.yAjm�,�3V0f,�3V././0t36uv.fOQg6,�p¯0f;In¢.fl@,�g=OQ,�P�mT;IO�>c.e;6pn3V.fl@,�n3V.fO7u�365c,��ku�OQ,�>auvA*�9q/,�,G,6CÂs@C�ùa36>k���6� � ��wV.fl@,�A�la3^g6,G.fl@,U<?O7qf36<@gV36>c.f3Vs6,U;6pjma0t;=<ax?u�O7>@s�<aO7q/./[email protected];I>W�p¯xa>?uv.fOQ;I>�,�qf.fO7n3V./;60tq4.fla3V.D3V0f,&>@;6.4uv;I>?q/./0t36O7>@,�< ,�OQ.fl@,�04./;�57OQ,�hT,�.yPz,�,�>ï�"36>a<���;604./;ih�,�n*;I>@;6./;I>a,O7>auv0f,�36qfO�>@s@C«��>�h�;6.fl�.fl@,�q/,R0f,�q/m�,�uv.fq�w6�436<a3V0t3�AI3��cH�3V.fqf;I>Zn*,�.fla;=<aq-3V0f,�qfx@m�,�0tOQ;60^w�<@,�q/m�OQ./,U.fl@,�O70r0t3V.fla,�0573V0fs6,Uh�O736q�C-d�;60f,�;�g6,�0�wcOQpW;I>@,zm?36qfq/,�qr./;2laO7sIl@,�0/��;60t<@,�0rs6,�>@,�0t3657O�qf3V.fOQ;I>aq};[email protected],GSUx�36>a<��I;I>@,�q«3Vm?ma0f;I36utl�wqfxautl�36q�n*,�.fl@;W<aq�h?36q/,�<ï;I>�5Q;=u�365Ám�;I5QAW>@;InO�365«./,�u�la>aO7�=x@,�q�9q/,�,���� ���*ù?36>�36>a<��DO �/h�,�57q&���6�6úI��wr.fla,�>.fl@,*øÆ>@;I>W��<?O7q/./0tOQh�[email protected];I>m?0f;6m�,�0f.fOQ,�q�£Wp¯0f;InñP�laO�utli.fl@,�A�qfxWJ�,�0)h�,�uv;In*,�,�g6,�> n*;60f,�;6pÁ3*ma0f;6h�5Q,�n�C

��> .fl@,�ma0f,�qf,�>c."m?3Vm�,�0ZPR,�qfx@s6s6,�q/.i.yPz; >@,�P ./,�u�la>aO7�=x@,�qZ.fla3V.�573V0fs6,�5QA ;�g6,�0tuv;In*,�.fl@,�qf,ï<?O��*�u�xa5Q.fOQ,�q�C ~)l@,��a0�q/.�w�5Q;=u�365�5Q;6sIO7q/.fO�u�<aO7q/./[email protected];I>�,�q/.fO7n3V.fO7;I>}w�ma0f;W<axauv,�qi,�q/.fO�n3V./;60tq ;6p&3V0th?OQ./0t3V0tO�5QAlaOQsIlý;60t<@,�0*P2laO7utlÿ3657PR3^A=qZ57OQ,iq/./0tO7uv.f5QA�h�,�.�PR,�,�>ü��36>a<#�VCÿ��>ÿq/m?O70tOQ.�wG.flaO�q*3Vmama0f;I36u�l O7q&0f,�573V./,�< ./;0f,�uv,�>c.f57Ac��O7>j./0f;W<axauv,�<ý5Q;Wu�365Rm?3V0t36n*,�./0tO�uZn*,�.fla;=<aq�p¯;60<@,�>aqfO7.�A�,�q/.fO�n3V.fOQ;I>}þ�q/,�,ip|;60*,v¡@36n*m?57,�BR;6m�36q�����6���I��w��WO7n;I>@;VJ �����6�6ú=w��W,�uv.fOQ;I> � C��j��w«1��/;60f.�36>a<��I;I>@,�q*�����6�! 6�D36>a<ïE�;I36<@,�0k�����6�! 6��C Dx@0�q/,�uv;I>?<n*,�.fl@;W<�O7q�36>ÿøÆ36<��fxaq/./,�<�£«g6,�0tqfO7;I>�;6pe.fl@,"�236<?3V0t3�AI3��cH�3V.fq/;I>ü,�q/.fO7n3V./;60^C'�y.�O7q�<@,�qfOQsI>@,�<�./; 0f,�m?0f;V�<axauv,*.fl@,kqtx@m�,�0tOQ;60Dh?O736qDma0t;6mT,�0t.fOQ,�qD;6pe5Q;=u�365�5�O7>@,�3V0�n*,�.fl@;W<aq�wrP�laO757,�ma0t,�q/,�0fgWO7>@si.fl@,ma0t;6mT,�0t.�A�.fl?3V..fl@,��436<a3V0t3^AI3��cH�3V.fq/;I>�,�q/.fO�n3V./;604O�q�365QP�3�AWq23Z<aO7q/./0�[email protected];I>"p9xa>auv.fOQ;I>�CR��.2O�q)h?36q/,�<�;I>�PR,�OQsIlj./,�<}wT;60

Page 4: Methods for Estimating a Conditional Distribution Function ...

h?O736q/,�<}w@h�;=;6.fq/./0t3Vm'n*,�.fla;=<aq�þaq/,�,"��3V0fh�,�36>a<#�R,�0f.f36O75z�����6���I�)36>a<�1236575}36>?<'+G0f,�qt>@,�575G�����6�! 6��C~)l@,2ma0f;6m�,�0f.fOQ,�q�;6p}m�;IqfO7.fOQg=O7.�A*36>a<kn;I>@;6./;I>aO7u�OQ.yA3V0f,4m?3V0f.fO7u�xa5�3V0t5QA�36<ag�36>j.f3Vs6,�;IxaqeOQp�;I>@,DO7qGs6;IO�>@s

./;�O7>jg6,�0f.U3�uv;I>a<?OQ.fOQ;I>a365@<aO�q/./0tOQh?xa.fOQ;I>�,�qf.fO7n3V./;60U./;�ma0f;W<axauv,e36>,�q/.fO�n3V./;60U;6p}3�uv;I>a<?OQ.fOQ;I>a365@�=xa36>j.fO75Q,6C�%$U3V0t5QAZPz;60t�ZO7>".fl@,�573V././,�0�3V0t,�3*O7>au�57xa<a,�qG.fla3V.e;6p&�Rl?3V./.f36utla3V0fAI3Z36>a<'�D36>@s6;6m�36<alcAI3^A������6�V�c��wT�6;I>a,�q36>a<'1436575U�����6�V�c�236>a<(�Wla,�3V.fl@,�0236>a< d�3V0f0t;I>������6�V�c��C ��)DO��ku�xa57.fOQ,�q)uv;In*m?xa.fO7>@s�=xa36>c.fO�5Q,�,�q/.fO7n3V./;60�qh?36q/,�<�;I>'<?O7q/./0tOQh�[email protected];I>Z,�q/.fO7n3V./;60tq�.fla3V.�3V0f,�>@;6.e.fl@,�nq/,�57g6,�q�<aO7qf./[email protected];I>kp9xa>auv.fOQ;I>?qela3�g6,�h�,�,�>'<?O7q��u�xaqfq/,�<�hjA"SU3V;������6���I��C2~)l@,�A�O7>?u�57xa<@,D,v¡@O7q/./,�>auv,�;6pÁn�xa5Q.fO7m?5Q,�q/;[email protected];I>aq�Ced';60f,�s6,�>@,�0t365757A6w?ma0f;6h�5Q,�nqO7>cg6,�0t.fO7>@s <?O7q/./0tOQh�[email protected];I>ï,�q/.fO7nk3V./;60tq&.fla3V.&3V0f,�>@;6.�n;I>@;6./;I>@,";60&uv;I>?q/./0t36O7>@,�<�./;ï57OQ,"O7>�.fla,"O7>j./,�0fgV365* � ô �,+-la3^g6,�h�,�,�>�36<a<@0f,�qtq/,�<�h=A�B�l=x�36>a< Bel@,�>@s������6���I��C

ª257.fl@;Ix@sIl;Ixa0UO7>j./,�0f,�q/.zO�>uv;I>a<aOQ.fO7;I>a365a<aO7qf./[email protected];I>�,�q/.fO�n3V.fOQ;I>P�36qRn*;6.fOQgV3V./,�<kh=A&.fl@,�ma0t;6h?5Q,�n;6pGma0f,�<aO�uv.fOQ;I>'p¯0f;In .fO7n*,�qf,�0tOQ,�q4<a3V.f3Ww�Pz,&qfla36575rO7>j./0f;=<?xauv,�;Ix@0Dn*,�.fl@;W<aq4O7>�3"n*;60f,�s6,�>@,�0t365Áq/,�./.fO�>@sP�laO7u�lk36<anO7.fqU.fO7n,4q/,�0�OQ,�qzn;=<@,�5�57O7>@s�36q�3�q/m�,�u�O7365?u�36q/,6C� [email protected],�;60f,�.fO7u�365T0f,�qfxa57.fq�wj./;=;@wWP�O7575ap|;Wu�xaqz;I>.fl@,�s6,�>@,�0t365«uv;I>c./,v¡W.�C

~)l@,zm?3Vm�,�0rO7qr;60fsI36>aO7qf,�<�36q-p¯;I575Q;^P2q�C«��>-�=,�uv.fO7;I>/.�PR,RO7>j./0f;W<axauv,G;Ixa0-n*,�.fla;=<aqrp¯;60r,�q/.fO�n3V.fOQ;I>�;6p?3uv;I>a<aOQ.fOQ;I>?365@<aO7q/./[email protected];I>}Crª�h�;=;6.fq/./0t3Vm"qfutl@,�n,�p¯;60zutla;j;IqfO�>@s�h?36>a<aP�O7<@.flaqÁO7qU3657q/;�sIOQg6,�>�CÁ�4xan*,�0�O7u�365,v¡W36n*m�5Q,�qGO7>jg6;I5QgWO7>@sDh�;6.flqfO7n�xa573V./,�<*n*;W<@,�57qU36>a<*0f,�365K��<?3V.f3�3Vmam?57O�u�3V.fOQ;I>aq�3V0f,)0t,�mT;60t./,�<O7>0�=,�uv.fOQ;I> � Cª u�36q/,*q/.fxa<@AiP�O7.fl 3"n�x?5Q.fOQgV3V0tO73V./,�m?0f,�<aO7uv./;604O7q2O�>au�57xa<@,�<'.fl@,�0f,6C1�=,�uv.fOQ;I>(�i<a,�qfuv0tOQh�,�q�uv;I>jg6,�0fs6,�>auv,0t3V./,�q&36q�PR,�575G36q&36q/AWn*ma./;6.fO7uZ<aO7q/./0�[email protected];I>�ma0t;6mT,�0t.fOQ,�q�;6pe.fl@,Zma0f;6m�;Iq/,�<�,�qf.fO7n3V./;60tq�C ª2575G./,�utla>aO�u�3653V0fsIxan*,�>j.fq�3V0f,�sIO7g6,�>�O7>i.fl@,�ª2mam�,�>a<aOQ¡TC

2 3 4Áè65&ê�ë*ê87fê:9<;H�,�36qfqtxan*,�.fla3V.ï<a3V.f3�3V0f,�3^g�36O75�3Vh?5Q,�O7>û.fl@,�p¯;60tn ;6p3�q/./0tO7uv.f57A qf.f3V.fOQ;I>a3V0fAûq/./;Wutl?36q/.fO7u�m?0f;=uv,�qtqój�¯ò=� ô ð���t÷Iw�P�la,�0f, ð��O7q"3�qtu�36573V0�36>a<üò=��O7q"3?>I��<aO7n*,�>aqtOQ;I>a365)g6,�uv./;60^C �23V.fx@0�36575QA6we.flaO7q"O7>au�5�xa<@,�q.fl@,*u�36q/,*P�l@,�0f,�.fl@,&m?36OQ0�q��¯ò=� ô ð���23V0f,*O7>a<a,�mT,�>?<@,�>c.436>a<ïO7<@,�>j.fO7u�36575QA'<?O7q/./0tOQh�x@./,�<}C�H�,*P2O7qfl ./;",�q/�.fO7n3V./,".fl@,"uv;I>?<aOQ.fOQ;I>a365U<aO7q/./[email protected];I>ïp9xa>auv.fOQ;I>?@G��ACB �}�EDGFk�9ð �1H AIB ò � �J����C���>�.fl@,Z.fO�n*,Zq/,�0�OQ,�quv;I>c./,v¡W.�waò=�«.yAjm�O7u�36575QA<@,�>a;6./,�qe3�g6,�uv./;60�;6pr573Vs6s6,�<igV3657x@,�qR;6prð��wWO�>kP�l?O7utl"u�36q/,1@G� õ B ���RO�qU.fl@,Dma0t,�<aO7uÊ�.fOQg6,�<?O7q/./0tOQh�[email protected];I>i;6pGð�GsIOQg6,�> ò=����«C2�yp�PR,�P)0tOQ./,=K����LT�9ð�� H A@�e.fl@,�>(M"�NK��OB ò=���P�}�Q�R@G��ACB �}��w36>a<'q/;*;Ix@0�,�q/.fO7n3V.fOQ;I>'ma0f;6h?5Q,�nñnk3�Aih�,�g=OQ,�PR,�<'36qe0t,�s60f,�qfqfOQ;I>';6p�KS�r;I>'ò=��C

~«;�qtO7n*m?57O7p|A�<aO�qfu�xaqfqfO7;I>�PR,)O7>j./0f;=<?xauv,�;Ix@0Gn*,�.fl@;W<aq�36>a<*<@,�g6,�57;6m.fl@,�;60fA�;I>a5QA�O7>&.fl@,)u�36q/,eP�la,�0f,ò=�ÁO�qe3qfu�36573V0��%TU�V����>/� �^��CU~)l@,�n�xa5Q.fOQgV3V0tO73V./,�u�36q/,�P�O7575Th�,�O75757x?q/./0t3V./,�<iO7>'�=,�uv.fOQ;I> � C

.

Page 5: Methods for Estimating a Conditional Distribution Function ...

W�XUY Z<[S\^]C_ _N[I`badcfe�ad\hgjike�lm[Snmcù@;60i�@¡=,�<oA�w�P)0�OQ./,'Fk���}�#�p@G��ACB �}�*36>a<�36qfqfxan,�.fla3V.�F�la36qrq0s���uv;I>j.fO7>=x@;IxaqZ<@,�0tOQgV3V.fOQg6,�q�Cûªs6,�>@,�0t3657O7qf,�<�57;=u�365Á5Q;6sIO7qf.fO7u&n*;=<a,�5rp¯;60 Fk�����4l?36qD.fl@,&p|;60tnut4��� ôwv �xDzy&��� ôwv �|{cóc�x}oy���� ôwv �t÷Iw�P�la,�0f,y���~ ôwv �-<a,�>@;6./,�qG3�>@;I>a>a,�sI3V.fOQg6,ep¯x?>auv.fOQ;I>�P�laO7u�l&<@,�m�,�>a<aqr;I>*3Dg6,�uv./;60U;6p?m�3V0t36n*,�./,�0tq v � � v 8 ô�õ�õ�õ�ôwv�� �.fla3V.iøF0f,�ma0f,�qf,�>c.�£Á.fl@,igV3657x@,�q�;6p:Fk���}� ô F/��8d�v���}� ô�õ�õ�õ^ô F/� � � 8d��������C�1�,�0f,6w�øF0f,�ma0f,�qf,�>c.�£Gn*,�36>?q�.fl?3V.�wUp¯;60,�36utl�q/,��=x@,�>auv,-� 8 � �9� ô �^� ô � Mcô�õ�õ�õ�ô � � <a,�>@;6.fO7>@sZmT;6./,�>j.fO7365rg�365�x@,�q�;6p�Fk����� ô F/�|8d�����}� ô�õ�õ�õ�ô F=� � � 8d�t���}��w0f,�q/m�,�uv.fOQg6,�[email protected]@,�0t,�,v¡WO�q/. vI8�ô�õ�õ�õ�ôwv � qfxau�l�.fla3V.y���� ôwv ���}�y&��� ôwv � ��� 8 }�� M ����s����b} õ�õ�õ }#��q^� � � 8 � � ����s���� � � 8 }��@�OB �rs��SB � � 8 �36q"�����«C'ª20fsIxa3Vh�5QA .fla,ZqfO7nm?5Q,�q/.�p9xa>auv.fOQ;I>?y P�OQ.fl�P2laO7utl�./; PR;60f��O7q"y&��� ôwv �1DJ�O� ���6L �w� wrP�la,�0f,� ��� ôwv ��� vc8 } v�M ��} õ�õ�õ } v � � � � 8 O7q�3�m�;I5QA=>a;InO7365-;6pe<@,�s60f,�,�q/s �VC"ùÁOQ./.fO7>as�.flaO7q�n*;W<@,�5�5Q;Wu�36575QA./;�O7>?<aO7u�3V./;60/��p9xa>auv.fOQ;I>ÿ<?3V.f3�5Q,�36<aqZ./;�36>�,�q/.fO7nk3V./;60��@G��AIB ���#D�t4�9� ô �v���� ��weP�l@,�0f, �vf��� <@,�>@;6./,�qZ.fl@,nO7>aO7nkO7q/,�0R;6p �� v þ|� ô A@��� ö ��¡ 8 ó�L��9ð� H A@�&s�t4�¯ò=�Cs�� ôwv �t÷ MC¢r£ �¯ò=�Cs���� ô �¤.=C7�^�¢ O7q�3Z�6,�0t>@,�5«p¯x?>auv.fOQ;I>}w ¢0£ ��~ �Q�R¥ � 8 ¢ ��~�{¦¥���w}36>a<h¥h§ �ZO7q23h?36>?<@P�O7<@.fl�CRH�,&u�36575r.flaO7q23Vmama0f;I36u�l¨ª©^«­¬¦¨6¨ª© �®T°¯²±¤T «8³ T�¯²±%´OTdµk¶·±¤T ©�¸ �,¯²±¤T�¹ ¬ ±¤T ©�¸ C�)4,�m�,�>a<aO�>@s�;I>ih�36>a<@P�O7<a.flkutla;IO7uv,6waOQ.�3657q/;&p¯xa0t>aO7qfla,�qUuv;I>aqfO�q��./,�>c.G,�qf.fO7n3V./;60tqU;6p�.fl@,2<@,�0tOQgV3V.fOQg6,�q�@&� � ����ACB �}��D �¤º6{¦ºk�}� � @G��ACB �}��wjO7>&.fla,)p|;60�n»�@&� � �t��AIB ���m�¼t½� � ���9� ô �v ��� �p|;60Q¾&��� ô�õ�õ�õ�ô q½s��VwWP�l@,�0f,8t � � � ��� ôwv �SD �¤º6{¦º���� � t2��� ôwv ��C���>kma0�36uv.fO7uv,6w �v ��� n3�AZh�,2uv;In*m?xa./,�<ZxaqtO7>@s.fl@,*øÆ<@;�P�>alaO75�5�qfO�n*m?5Q,v¡�£@365Qs6;60tOQ.flan �9qf,�,-�=,�uv.fOQ;I>����WC��"O7>�+G0t,�qfq:��± ¬¦¨ �����6��.I��C

H�,',v¡WmT,�uv.*.fla,�,�q/.fO7n3V./;60��@G��ACB �}��./;�la3�g6,�h?O736q�;6p2;60�<@,�0r¥ � 36>a<ýgV3V0tO736>auv,�;6p2;60t<@,�0 ��¿b¥T� � 8 wxa>a<@,�0D36>�36q/AWn*ma./;6.fO7u&qfu�l@,�n*,&P�l@,�0f,�¥h�z¥«��¿r�:� �i36>a<À¿b¥h�ÂÁ 36q�¿��ÃÁ C�ªon*;60f,*<@,�.f36O�5Q,�<36u�uv;Ixa>c.2;6pr.fl?O7qema0f;6m�,�0f.yAkP�O�575ThT,�sIO7g6,�>'O7>'�=,�uv.fOQ;I>Ä�@C

�y.iO7qZm�;IqfqfOQh?57,�./;��a.".fl@,�5Q;6sIO7q/.fO7u n*;W<@,�5�h=A n3V./0tOQ¡j��PR,�OQsIlj./,�< 57,�36q/.���qf�=xa3V0f,�qiO7> m�5736uv, ;6p�.fl@,uv0tOQ./,�0tOQ;I>ÿ3V.��¤.=C7�^��we0f,�Åa,�uv.fO7>@s�.fla,'<@,�m�,�>a<@,�>auv,�q/./0tx?uv.fx@0f,�;6p4.fl@,'ma0f;Wuv,�qfq"ó�ò � ÷ICü12;^PR,�g6,�0�w)OQp2.fl@,ma0f;Wuv,�qfqeO7q�PR,�3V�=5QA"<@,�m�,�>a<@,�>j.��N��� ���U3Vh?q/;I5�x@./,�5QA0f,�sIx?573V0�w@36q)36qfqfx?n*,�<�O7>Ä�=,�uv.fOQ;I>#�j��[email protected]?O7qela36q�;I>a5QA"3q/,�uv;I>a<W��;60t<a,�0),vJT,�uv.2;I>�m�,�0fp¯;60tn36>auv,6C

 Dx@0�x?q/,�;6pÁ.fl@,�5Q;6sIO7qf.fO7u�n*;W<@,�5�l@,�0f,�O�qe0f,�nO7>?O7qfuv,�>j.e;6pÁn,�.fl@;=<?qe,�n*m?5Q;�A6,�<�O7>�uv;I>?>@,�uv.fOQ;I>'P2OQ.flh?O7>a3V0fA�u�l@;IO7uv,en*;W<@,�57q�CÁ~)l@,�0t,6w�;I>a,R;6h�q/,�0fg6,�qÁ0f,�q/m�;I>aqf,zgV3V0tO73Vh?57,�q-ð�a.fla3V.�n3^A�.f3V�6,e;I>?5QA�.fl@,�gV3657x@,�qÁ�36>a<Z�Vw6P2OQ.fl"Fk�9ð�b���®B ò=�b�����m�PÆ�ó²Ç������t÷IwcP�l@,�0f,½ÆüO�qr32�=>a;^P�>�57O7>@�4p9xa>auv.fOQ;I>�36>a<�>@;I>@m?3V0t36n,�./0tO7u;60�q/,�nOQm�3V0t36n*,�./0tO7u�36qtqfxan*ma.fO7;I>aqe3V0f,�n36<a,�3VhT;Ixa.½Ç�CÈ�=,�,�p¯;60),v¡@36n*m?5Q,�d 3V.|É��=O�>������6��.I��w�ª2la>�36>a<d�36>aqf�=O4�����6� � ��wmÊ�5Q,�O7> �����6� � ��36>?<�ª2l?>������6���I��p|;60�PR;60f��O7>�,�uv;I>@;In,�./0tO7u�q�w�36>a<ýB�ljx�36>a<�B�la,�>@s

Page 6: Methods for Estimating a Conditional Distribution Function ...

�����6���I�-p|;60�<aO�qfu�xaqfqfO7;I>�;6p?h�O7>a3V0fA�utla;IO7uv,�p|0f;In�3Dn*;60f,eq/.f3V.fO�q/.fO7u�365=g=O7,�P)m�;IO7>c.�CS�WO7>auv,zPz,e<@;D>@;6.�36qfqfx?n*,.fla3V.r@G��AIB ���kO7quv;I>j.fO7>=x@;IxaqkO�>�Aý.fl@,�>}weO7>�u�36q/,�qkP2l@,�0f,ÀÆ O7q.fla, O7<@,�>j.fOQ.yAý36>?< ;I>a5QAýqfn*;=;6.fla>@,�qtq36qfqfxan*m?.fOQ;I>aq�3V0f,n36<a,;6p�Ç�wr.fl@,kn*,�.fla;=<aq�la,�0f,k36>a<�O7>ï.fla,k>@,v¡W.�qfx@h?qf,�uv.fOQ;I>�n3�Aïh�,*gWOQ,�Pz,�<�36q3n*,�36>aq�;6p-,�qf.fO7n3V.fO7>@s*m?0f;6h?3Vh?O75�OQ.fOQ,�q�O7>ih?O7>?3V0fAZu�l@;IO7uv,�n;=<@,�5�q�w@O7>�.fl@,�uv;I>j./,v¡W.2;6pGB�l=x'36>a< B�la,�>@s�����6���I��CW�XªW Ë�n�̦Ímcfe�i�nzÎ?]6nm]6Ï!]·Ðb]�ÑÓÒÔ]e!c�[bÕzic�e!adgj]Öe�[IÏE�,�. � ��� � �����}��w}p|;60*� H ¾ H ¿�w}<@,�>@;6./,&Pz,�O7sIlc.fq�¯p9xa>auv.fOQ;I>?q�;6pG.fla,�<a3V.f3"ò 8�ô�õ�õ�õ�ô ò*ö?w�36q4Pz,�5�5r36qD;6p���RP�O7.fli.fl@,�ma0f;6m�,�0f.yAZ.fla3V.�,�36utl � �&×ü�WwÖØ � � �I����36>a<

ö  ��¡ 8 � �/�������¯ò=�Is���� ¢0£ �¯ò=�Cs��}��� � õ �¤.=CV.I� 4pGuv;Ix@0tq/,6w � ��£FqDqf3V.fO7q/p¯AWO7>@s.fl@,�qf,�uv;I>a<?OQ.fOQ;I>aq23V0f,*>@;6.4x?>aO7�=x@,�5QAi<@,��?>@,�<}wT36>a< Pz,&q/m�,�u�OQp¯A�.fl@,�n uv;I>@�u�O7q/,�5QAZhjA�36q/�WO7>@s*.fla3V.�Ù � � � h�,D36q2573V0fs6,�36q�mT;IqtqfOQh?5Q,Dqfx@h@��,�uv.e./;.fla,�uv;I>aq/./0t36O�>c.fq�C�)2,���>@,

Ú@G��AIB ����� Ø ö��¡ 8 L��9ð� H A@� � �/����� ¢r£ �¯ò=�Cs����Ø ö��¡ 8 � � ����� ¢0£ �¯ò � s���� õ �¤.=C � ���;6./,"m?3V0f.fO7u�x?573V0t5QA�.fla3V.�� H Ú@G��AIB ��� H �k36>?< Ú@üO�q�n*;I>@;6./;I>a,"O7>�A�C�H�,iqfla365�5Gqfl@;�P O7>��=,�uv.fOQ;I>?�.fla3V. Ú@�O7q��a0tqf.���;60t<@,�0e,��=xaOQgV365Q,�>c.�./;357;=u�365}57O�>@,�3V0�,�q/.fO7n3V./;60�w@P2laO7utl�<a;j,�qe>@;6.e,�>V��;�AZ,�OQ.fla,�0);6p«.fl@,�qf,ma0f;6m�,�0f.fOQ,�q�C

�y.)O�q�mT;IqtqfOQh?5Q,4p¯;60).fl@,�,�q/.fO7nk3V./;6023V.��¤.=C � �e./;k36qfqfxan,4.fla,�p|;60�nñ�®{��Ww�<ax@,�./;>a;<a3V.fxanñò=��5QAWO7>@sO7>ï.fl@,k5Q;Wu�365�P�O�>a<@;^P�Ckd';60f,ks6,�>@,�0t36575QA6w-q/m?3V0tqtOQ.�A�;6pe<@,�qfOQsI>�m�;IO7>j.fq�u�36>�qf;In*,�.fO7n*,�q�hT,3�<aO��ku�xa57.�A6C1�;�Pz,�g6,�0�w�.fl?O7q�O7q"s6,�>@,�0t365757A�q/;In*,�P2la3V.'5Q,�qfqi;6p&3ýma0f;6h?57,�n p¯;60�.fl@,�n*;W<aOQ�?,�<��436<a3V0t3^AI3��cH�3V.fq/;I>,�q/.fO7n3V./;60R.fla36>Zp|;60R5Q;=u�365�57O7>@,�3V0U,�q/.fO7n3V./;60tqRO7>*.fla,2qf36n*,4q/,�./.fO7>@s@wWO7>*.fl?3V.Rq/m�3V0tqfOQ.yA�./,�>a<?qU./;�ma0f;W<axauv,qfn36575ju�xaq/m?qrO7>�.fl@,R,�q/.fO7nk3V./;60 Ú@ÁwV0t3V.fla,�0r.fla36>�.fl@,�573V0fs6,�Å?xauv.fxa3V.fOQ;I>?qr36qfqf;=u�O73V./,�<�P�OQ.fl�<@,�qfOQsI>�q/m?3V0�qfOQ.�Ap|;60�5Q;Wu�365«m�;I5QAW>@;InO�3657q�C�+U0f;6h?5Q,�nq2P�OQ.fl <a3V.f3iq/m?3V0tqf,�>@,�qfq�wTp|;60D,�OQ.fla,�0#�@�;60 Ú@Áw}n3�A'h�,�;^g6,�0tuv;In,*hjA5Q;=u�365�5QA�O7>auv0f,�36qfO�>@s�.fl@,Rh?36>a<aP�O7<@.fl}w^;60-h=A�[email protected]>@s)>a,�P�<@,�qtOQsI>�m�;IO7>j.fq�gWO734O7>j./,�0fm�;I573V.fOQ;I>}þVq/,�,x�=,�OQp¯,�0f.36>a<À�D36qtq/,�0�����6�6úV3WwÂhT�436>a<�1436575r36>a< ~-x@0t5�36utl������6�! 6��p¯;604<?O7qfu�xaqfqtOQ;I>�;6p�.fl@,�q/,�3Vmama0f;I36u�l@,�qDO7>�n;60f,uv;I>cg6,�>j.fOQ;I>a365«ma0f;6h?5Q,�nkqeO7>cg6;I57g=O7>as&>a;I>@m?3V0t36n*,�./0�O7u40f,�s60f,�qfqfO7;I>}C

ª2>a;6.fl@,�0P�3�Aý;6p2gWOQ,�P�O�>@s .fla,'h?O736q/,�<�h�;=;6.fq/./0t3Vm ,�q/.fO�n3V./;60 Ú@#O7q*36qZ3�5Q;=u�365e5�O7>@,�3V0*,�q/.fO7nk3V./;60O7>�P2laO7utl�.fl@,&PR,�OQsIlj.fqDp|;60D.fl@,*5Q,�36q/.���qt�jxa3V0t,�q�q/./,�m�3V0f,&.f3V�6,�>�./;�h�, � � ����� ¢r£ �¯ò � s?����w}0t3V.fla,�04.fl?36>qfO7n*m?57A ¢0£ �¯ò=�bs?����w�p¯;60*� H ¾ H ¿�C�~«;�3Vmam?0f,�u�O73V./,&P�ljA�.flaO7qDO7qDq/;@w}PR,*0f,�p¯,�0D./;�.fl@,*<@,��?>aOQ.fO7;I>�;6ps6,�>@,�0t365�5Q;Wu�365�57O�>@,�3V0z,�qf.fO7n3V./;60tqRsIOQg6,�>"h=Akùa36>�36>a<#�DO �/h�,�57q2�����6�6ú=wam«C^.V�c��wa36>a<">@;6./,D.fla3V.eO7>kg=OQ,�P ;6p

Page 7: Methods for Estimating a Conditional Distribution Function ...

�¤.=CV.I��w?P�OQ.fl'.fl@,�qfx@s6s6,�q/./,�< utla36>as6,�;6p-Pz,�OQsIlj.fq�wa.fla,�OQ0),�q/.fO7nk3V./;60ÄÛÇÄÜD0f,�<axauv,�q)./;ÛÇÄÜ6�������ÞÝ ö ��¡ 8Qß �f�����àL��9ð� H Aa��áIâjÝ

ö ��¡ 8½ß �/������á ôP�l@,�0f,

ß �/������� � �����}� ¢0£ �¯ò=�Cs��}�ö ã ¡ 8 � ã ����������s�ò ã � MC¢0£ ���rs�ò ã � õ

~)l@,�0f,�p¯;60f,6w ÛÇ Ü � Ú@G��AIB ����CBR;In*m?xa.f3V.fOQ;I>�;6p-.fl@, � ��£Fq)O7qeqfO�n*m?57OQ�?,�<kh=AZ.fla,�p¯36uv.�.fla3V.

� �����}�S��¿ � 8 ój�m}�ä�����s�ò=��� ¢0£ �¯ò=�6s����t÷ � 8 ôP�l@,�0f,0ä �93ip9xa>auv.fO7;I> ;6pz.fl@,*<a3V.f3�36>a<ï;6p����4O7qDxa>aO��jx@,�57Ai<a,��?>@,�<�hjAý�¤.=CV.I��C&�y.�O7q4,�36qfO�5QA�uv;In*m?xa./,�<xaqfO7>@s*3�2,�P)./;I>W��:23Vm?laq/;I>�3V0fsIxan*,�>j.�CRBR;I>a<?OQ.fOQ;I>��¤.=CV.I�e,�>?qfx@0f,�q�.fla3V. Ø � � � ���VCW�Xªå æ�]6Õ�nSç(adnSe!lz\®lm[baU\^i+-3V0t.fO7u�xa573V0t57AkO7>i.fl@,�.fO7n,Dqf,�0tOQ,�qeu�36q/,6wT<@,�0tOQgWO7>@s�36q/A=nma./;6.fO7u�36575QAZ;6ma.fO7n365�h�36>a<@P�O7<a.flaqUp¯;60e,�OQ.fl@,�0�.fl@,5Q;=u�365�5Q;6sIO�q/.fO7u4;60eh?O736q/,�<"h�;=;6.fq/./0t3Vm'n*,�.fl@;W<aq�O7q�3&./,�<aOQ;Ix?qRnk3V././,�0�C�è4qfO7>@s�m?57xasV��O7>Zn,�.fl@;=<?qz0t,��jxaO70f,�q,v¡=m?5�O7u�OQ.�,�q/.fO�n3V.fOQ;I>�;6p)uv;In*m?5Q,v¡�p9xa>auv.fO7;I>aq�xaqtO7>@s�<@,�m�,�>a<a,�>c.�<?3V.f3WþzxaqfO�>@s'.fl@,"h�;j;6.fq/./0�3Vm�u�36575�q�p¯;60q/,�5Q,�uv.fOQ;I>ÿ;6pDqfx@h�qfO7<aO73V0tAïqtn*;j;6.fl?O7>@sïm?3V0t36n*,�./,�0�q36>a<ÿ0f,�qt36n*m?57O7>as�;6p4.fO7n*,v��q/,�0tO7,�q<a3V.f3Wþ)36>a<ÿxaqtO7>@suv0f;Iqfq���gV3657O7<a3V.fO7;I>�<@,�n36>a<aq�q/,�57,�uv.fOQ;I>�;6p-.fl@,�36n*;Ixa>j.e;6p�<a3V.f3&.fla3V.�3V0f,�57,�p|.�;Ix@.�CÈ�@xautl�uv;In*m�5Q,v¡WO7.�AiO7q3V0fsIxa3Vh?5QAï>@;6.)�/xaqf.fOQ�a,�<}w�>@;6.�5Q,�36q/.�h�,�u�36xaqf,.fl@,k.f3V0ts6,�.�p9xa>auv.fOQ;I>�FZ����� �é@G��AIB ����O7q�;6p¯./,�>�3Vmama0t;�¡@OK�n3V./,�5QAZn;I>@;6./;I>@,�36>a<iq/;l?36q�;I>a5QAZ5�O7nOQ./,�<Z;6mam�;60f.fxa>aO7.�A*p¯;60)uv;In*m?5Q,v¡"hT,�l?3�gWOQ;Ix@0�C�ù@;602,v¡W36n*m�5Q,6w·FO7q�,v¡W36uv.f57A'n*;I>@;6./;I>@,�O7p«.fl@,��/;IO7>j.)<aO7q/./0�[email protected];I>k;6p)�¯ò=� ô ð����O7qe>@;60tnk365�C��>?q/./,�36<}w«PR,Zqtx@s6s6,�q/.�36>�3Vmama0f;^¡WO7nk3V./,m?3V0t36n*,�./0�O7u*n*,�.fl@;W<}wr36q�p|;I5�5Q;^P�q�CH�,k�a.�3�m?3V0t36n*,�./0�O7u

n*;=<a,�5ð�C�¼êàÜm}�ê 8 ò=�k} õ�õ�õ }�êàë^ò ë� }�ìIíw� ô

P�l@,�0f, í|�-O7q�q/.f36>a<a3V0t<i>@;60�n365�w^êîÜ ô�õ�õ�õ�ô êàë ô ìï3V0f,D,�q/.fO7n3V./,�<ip¯0f;In .fl@,�<a3V.f3Wwa36>a<#ï"O7q�<@,�./,�0tnkO7>@,�<ZhjAª��fB4C@H�,�p¯;60tnñ3*m?3V0�36n*,�./0tO7u4,�q/.fO7nk3V./;60�ð@G��AIB ���zh?36q/,�<';I>�.fl@,�n*;W<@,�5�CS�RAid�;I>j./,&B�3V0t57;&qtO7n�x?573V.fOQ;I>p|0f;In .fl@,�n*;W<@,�5�w@PR,�uv;Inm?x@./,�3khT;=;6.fq/./0t3Vm g6,�0tqfOQ;I>';6p�ó^ð-ñ8 ô�õ�õ�õ^ô ð/ñö ÷�h?36qf,�<';I>'sIO7g6,�>';6h?q/,�0tg�3V.fOQ;I>?qó�ò 8�ô�õ�õ�õ^ô ò*ö�÷Iw�36>a< .fl@,�>auv,�3h�;j;6.fqf./0t3Vm g6,�0�qfOQ;I>��@Iñ£ ��ACB �}���Ô�@IñV��AIB ���);6p1�@G��ACB �}��wT<@,�0�OQg6,�<'p¯0f;In��¤.=C7�^�P�OQ.flZój�¯ò=� ô ð����t÷)0f,�m?5736uv,�<&h=Aój�¯ò=� ô ð/ñ� �t÷IC�~)l@,�h�;j;6.fq/./0�3Vm�,�qf.fO7n3V./;60G;6p�.fl@,e3Vh?q/;I57x@./,e<@,�gWO73V.fOQ;I>�,�0f0t;60;6p �@G��AIB ���eO7q ò

�¤¥�þ|� ô Aa�m�¼M * B¤�@ ñ£ ��AIB ���Ssð@G��ACB �}��B�Btój�¯ò � ô ð � �t÷�+ õ�

Page 8: Methods for Estimating a Conditional Distribution Function ...

B�l@;=;Iq/,Ä¥�� �¥«��� ô Aa��./;�nO�>aO7nO7qf,ò�¤¥�þ|� ô Aa��C��=;In*,�.fO�n*,�q&Pz,'x?q/,i.fl@,#�a��<@,�m�,�>a<a,�>c.&h?36>a<aP�O7<@.fl�¥«������P�laO7u�l�nO7>aO7nkO7q/,�q ò

�¤¥�þ|���m�ôó ò �¤¥}þ|� ô A@��ð@R��ACB �}�à>!A õ �¤.=C��j�~)l@,�3Vh�;^g6,�3Vm?ma0f;I36utl u�36>�3657qf;*hT,�3Vm?m?57OQ,�<"./;ku�l@;j;IqtO7>@s0¥�p|;60),�qf.fO7n3V.fO7>@s Ú@G��AIB ����C��>�.fl@,R,�g6,�>c.�.fl?3V.-PR,�3V0f,zPR;60f�WO7>@s4P�OQ.fl�.fO7n*,v��q/,�0tO7,�q-<?3V.f3��N��� ���Áò=�b� ð���kõ�p¯;60�q/;In*,ÈÇö×û�^��w6PR,

ma0f;6m�;Iq/,&36>�365Q./,�0t>a3V.fOQg6,*0t,�qf36n*m?57O�>@skqfu�l@,�n*,36qDp¯;I575Q;^P2q�C�ª4qfqfxan*,&.fla3V.D.fl@,*<a3V.f3�ó^ð �kõÈ� 8 ô�õ�õ�õ^ô ð ö ÷0f,�ma0f,�q/,�>j.23Zq/,�sIn*,�>j.D;6pG3��D36xaqtqfO736>�36xa./;60f,�s60f,�qfqfO7;I>}Cx$Uqf.fO7n3V./,�O7.fq)m?3V0t36n,�./,�0tq�w�36>a<�0t,�qf36n*m?5Q,�.fl@,q/,�sIn*,�>j.ïó^ð-ñ�kõQ� 8 ô�õ�õ�õ�ô ð-ñö ÷�p¯0f;In .fl@,�m?3V0t36n*,�./0tO�u�n;=<@,�5�C�~)la, h�;=;6.fq/./0t3Vm ,�q/.fO7n3V./;60Ä@Iñ£ ��ACB �}�ZO7qu�3657u�xa573V./,�<'x?qfO7>@s&.flaO7qeqf,�sIn*,�>c.�wT36>a<�.fl@,�>�qfx@h?q/.fO7.fx@./,�<�O7>j./;*.fl@,�p¯;60tn�x?573&3VhT;�g6,�p¯;60

ò�¤¥}þ|� ô Aa��C

÷ ø¢ì=ùö4Ué�îfíSú<7Àû&é}ê:û�4GéTè�îO4�üå�XUY ý�aUgoÍm_N]Öe!aN[ÓÕôcfe!ÍmnmaUi�cH�, uv;In*m?3V0t,�< gV3V0tOQ;Ixaq*,�qf.fO7n3V./;60tqk;6p4.fla,�uv;I>a<aOQ.fO7;I>a365e<aO7q/./0�[email protected];I>�p9xa>auv.fOQ;I>�@G� õ B õ �.fl@0f;Ix@sIl .�PR;qfO7n�xa573V./,�<in*;W<@,�57q�wW;I>@,�P�O7.fl�O7>a<@,�m�,�>a<@,�>j.U;6h�q/,�0fgV3V.fOQ;I>aqe36>a<i;I>@,�P2OQ.fl�>@;I>a57O�>@,�3V0z.fO�n*,�q/,�0tOQ,�q�CÁ~�l@,,�q/.fO7n3V./;60tqZuv;I>auv,�0t>@,�<�3V0f,'.fl@,'�436<a3V0t3^AI3��cH�3V.fq/;I>#,�q/.fO�n3V./;60��9�2H#��wz.fl@,�5Q;Wu�365)57O�>@,�3V0*0f,�s60f,�qfqtOQ;I>,�q/.fO7n3V./;60k�9ErE-��wT.fl@,*36<��/x?q/./,�< �436<a3V0t3^AI3��cH�3V.fq/;I>�,�q/.fO7n3V./;60�9ª4��Hû��w�36>a<�.fl@,&5Q;=u�365Á5Q;6sIO�q/.fO7u�,�qf.fOK�n3V./;60tq2P�OQ.flÄq/�ô. �9E&�2�d.I�236>a<'q-� � �9E&�4� � ��C)ù@;60D,�36u�l�qtO7n�x?573V./,�<'qf36n*m�5Q,6w?.fl@,�m�,�0fp|;60�n36>auv,�;6p.fl@,�,�q/.fO7nk3V./;60)PR36q�,�g�365�xa3V./,�<�O7>i./,�0�nqe;6pGd',�36> ª�h�q/;I57x@./, )4,�g=O�3V.fOQ;I>'$U0f0f;60���d ª:)�$R�­þ

d ª:)�$�� Ø � B @�ÿ���A��|B ����Ss�@G��A��|B �����BàL��9� õ �6�@� H @G��A��|B ���� H � õ �6�6�I�Ø � LT�9� õ �6�@� H @G��A��OB ���� H � õ �6�6�I� ôP�l@,�0f,=@�ÿ�� õ B õ �D<@,�>@;6./,�q�36>�,�qf.fO7n3V./;60�;6p�@G� õ B õ ��w-36>a<�ój����� ô A����t÷k3V0f,&s60tO7<�m�;IO7>j.fq2P2laO7utl�P�O�575«h�,&q/m�,�uÊ�OQ�a,�<�573V./,�0�CZH�,kuv;I>a<ax?uv./,�<�.fl@,kqtO7n�x?573V.fOQ;I>ïO7>�.yPz;�qf.f3Vs6,�q�C"ùÁOQ0�q/.�w«PR,ku�3657u�xa5�3V./,�<�d�ª8)�$Uq�p|;60�.fl@,g�3V0tO7;IxaqR,�q/.fO7n3V./;60tq�;�g6,�0)s60tO7<"m�;IO7>j.fqU,�g6,�>?5QAZ<aO�q/./0tOQh?xa./,�<k36uv0f;Iqfq�.fla,4P2l@;I5Q,Dqf36n*m?5Q,Dq/m?36uv,6Czù@;60),�36utl,�q/.fO7n3V./;60�w?Pz,�x?q/,�<i.fl@,�;6ma.fO�n365�h?36>a<@P2O7<@.fli<@,��?>@,�<ih=A

¥�� � ���}���Pó¥�� � ��� ô Aa�à@G��ACB �}�à>!A ôP�l@,�0f,:¥ � � ��� ô Aa�GO7qG.fl@,2nO�>aO7nO7qf,�0-;6p}.fla,236q/AWn*ma./;6.fO7u2n*,�36>kqt�jxa3V0t,�<,�0f0f;60D�9x@mk./;��a0tqf.G;60t<@,�0Ê�Á;6p}.fl@,,�q/.fO7n3V./;60�CD~)laO�q)sIxa3V0t36>j./,�,�q�3Zp¯36OQ0Duv;In*m?3V0�O7q/;I>�36n*;I>@si<aOKJ�,�0f,�>c.4n*,�.fl@;W<aq�C �=,�uv;I>a<a5QA6wTPR,�<@,�n;I>W�q/./0t3V./,�<.fla,)xaq/,�p9xa57>@,�qfqÁ;6pT.fl@,)h�;=;6.fq/./0t3Vmkqtutl@,�n*,�p|;60Uu�l@;=;IqfO7>@s�h?36>?<@P�O7<@.fl?q«ma0t;6mT;Iqf,�<O7>0�=,�uv.fOQ;I>r.=C �hjA�,�g�365�xa3V.fO7>@s'd ª:)�$Uq�p|;60�q/;In*,*�@¡W,�<ïg�365�x@,�q�;6pÈ�«C&H�,kxaq/,�<ï.fla,��a��<@,�m�,�>a<a,�>c.Dh?36>a<aP�O7<@.fl �¥«���}�P�laO7u�l�nO7>aO7nkO7q/,�qD�¤.=C��j��CR~)la0f;Ix@sIl@;Ix@.�.flaO�qeq/,�uv.fOQ;I>'PR,�xaqf,�<i.fl@,-�D36xaqtqfO736>i�6,�0t>@,�5�C

ú

Page 9: Methods for Estimating a Conditional Distribution Function ...

-0.5 0

0.5

X-3-2

-1 0

12

3

Y

00.

20.4

0.6

0.8

1Z

(a) True conditional distribution

••

•• •

••

••

••

••

••

••

••

••

••

••

••

• •

••

••

•••

• •

•••

••

••

••

• •

••

• ••

••

••

••

• •

• •

• •

••

• •

• •

••

• •

••

••

••

• •

••

••

••

••

• •

•••

••

• •

•••

• ••

••

• •

••

••

••

•••

••

• •

••

• •

••

••

••

••

••

••

•••

••

••

• ••

•••

••

••

••

••

••

••

• • •

••

• •

••

••

• •

••

• •

••

••

• •

••

••

••

••

••

••

••

•••

(b) A sample of 600 observations

X

Y

-1.0 -0.5 0.0 0.5 1.0

-3

-2

-1

0

1

2

0.03

0.04

0.05

0.06

NW LL ANW LG-2 LG-3

(c) MADEs of estimators

ù-O7sIx@0f,i�¦þ����������� ��������������� ���������� �!���#"$%�'&!()�*�� ��+�,�� ����.-�@G��AIB ���/�0�����.-1��"2 ����3��546���27�89��7: �;:��<>=?�*@A ;�B ��*���BC����$7��� ������$��D7��+�* ��*��4��E ������F����$CG ������IHh� @G��AIB ����<J=K4K@MLN �O�"$��C���P�����#"$%�M�Q�'���%RG�-¿j� úV�6��.�S�67T���J�*�� ��+�,�� ������EUV W�6-0�� �;���)89�� �;X �;�MCS���Y��EA��G.ÁqfO7>«� � õ � �a��ú&�}��<Z=?C�@ A ;�[4\�S�*"2��� ��M�Q��]1L#^_��������� �;��`a�:7!���Q��O��:bdcF�� ������J�*�� ��+�,�� e�[=�`Fc�@GU5��SC���9f�+�2�\���/���e-��6�*�\�*�����g���* ����3�: e�M=�hih2@jUk�:7�l��0�* e�\7)`Fc�*�* ����,�� e��=�Lm`Fc�@GUno�SC\��p��6-:�q�� ���Cr���* ����,�� e�189�� �;�q?� .s=�hDt5uKv�@GU,���$7Xo�SC\��#��\-��+�* ���Cw���* ����,�� e�189�� �;q1� � =�hDt5uQx�@�<

Page 10: Methods for Estimating a Conditional Distribution Function ...

-0.05

0.0

0.05

0.10

ANWx=-.5

ANWx=.1

ANWx=.7

LG-2x=-.5

LG-2x=.1

LG-2x=.7

(a) Difference of MADEs

-0.10

-0.05

0.0

0.05

0.10

ANWx=-.5

ANWx=.1

ANWx=.7

LG-2x=-.5

LG-2x=.1

LG-2x=.7

(b) Difference of bandwidths

(c) Conditional distribution

x = -0.5

-3.0 -2.5 -2.0 -1.5 -1.0

0.0

0.2

0.4

0.6

0.8

1.0

(d) Conditional distribution

x = 0.1

0.0 0.5 1.0 1.5

0.0

0.2

0.4

0.6

0.8

1.0

(e) Conditional distribution

x = 0.7

1.0 1.5 2.0 2.5

0.0

0.2

0.4

0.6

0.8

1.0

ù-O7sIx@0f,-.àþ������/�o�� ������>�6�*�*�0� ��������a� �!���#"$%�'&!(,�*�* ����,�� ����.-�@G��AIB ���/89�� �;I4\�S�� ��� ��Q��"y4\���$7�89��7� �;:��<T=?�*@A ;�n46�S��"$o�� ��_�Q�# �;�k]FLm^_�5�p46�z�S�673��� �¥r�����D�/�����0�p �;�k]1L#^_�5�#4\�z���\73����¥�� � ������</=K4Q@ A ;�n46�G�*"$o�� ���Q� �¥«������sE¥ � � ���}��<a=KCQ@zb{=K�K@ A ;�#C���*Y��*�5���K"$�6�*�����{ ����.-3C\���27��� ������$��$7��+�* ��*��4�� ������m����$CG ������E��@G� õ B �}�\|} �;!��C�~����2�[� @G� õ B �}�\UV �;!�+������2�M� �!7Ql��0�� e�67F`��:7:������O:��bdc1�� ����������* ����3�: e�*Ua7:�z��;�67r����2�M� o�SC���Po�6-:�q�� ���C�*�* ����,�� e��=�q"� .j@�<

Page 11: Methods for Estimating a Conditional Distribution Function ...

�#��_$�>�Á®¯¥>�aCzE�,�.�xaqeuv;I>?qfO7<@,�0e.fl@,�qfO7n*m?57,4n*;W<@,�5ð�C� .ÁqtO7>�� � õ � �a��ú-ò=���C}�íw� ô

P�l@,�0f,�ó�ò=�y÷�36>a< ófí|�y÷�3V0f,D.�PR;&O�>a<@,�m�,�>a<@,�>j.Gq/,��=x@,�>auv,�qR;6p«O7>a<a,�mT,�>?<@,�>c.U0t36>a<@;In g�3V0�O73Vh?5Q,�qzla3�gWO7>@s&3uv;Inn*;I>"<aO7q/./[email protected];I>&P�O7.fl<@,�>aqfO7.�A'�&s�B �SB6;I> * s�� ô �,+�CU~�l@,�./0txa,2uv;I>a<aO7.fOQ;I>a365a<aO�q/./0tOQh?xa.fOQ;I>�p¯xa>?uv.fOQ;I>O7q�m?5Q;6././,�<'O�>�ù-O7sIx@0f,�I�93c��Czùa;60�,�36utl�;6pÁ.fl@, �I�6�qf36n*m�5Q,�qe;6pÁqfO�É�, ¿(�#úV�6���¯;I>a,�;6pr.fla,�n¢O7q)<@,�m�O7uv./,�<O7> ùÁOQsIx@0f,��I�¯h��/��wePz,�u�3657u�xa573V./,�<ü.fl@, d ª:)�$UqZP�OQ.fl .fl@,';6ma.fO7nk365eh?36>a<@P2O7<@.fl�¥�� � � õ �'�¯P2laO7utl�O7q*;6pqfO�É�,-¿ � 8?�Q��p¯;60�E&�2� � w�36>?<(¿ � 8?�Q��p¯;60�36575«.fla,�;6.fla,�0�n*,�.fl@;W<aq���C�H�,*,�q/.fO7nk3V./,�<�@G��ACB �}�);I>�3"0f,�sIx?573V0s60tO7<�<@,��?>@,�<�h=A�q/./,�m?q&�WCF�Iú! ï36>?<��WCF�!����O7>��?��36>a<�Ac��<aO70f,�uv.fOQ;I>aq�w�0t,�q/m�,�uv.fOQg6,�5QA6C�~)l@,"h�;�¡=��m?5Q;6.fq&;6pd�ª8)�$Uq�3V0t,ma0f,�q/,�>j./,�<�O�>�ù-O7sIx@0f,'�I�9u^��CZ~�l@,*g�3V0�O73V.fOQ;I>aq�;6p�.fl@,kd ª8)8$zq�p¯;60�.fl@,Z��H�w«E«EUw�ª2�2H36>a<ýE&�2�d.�n*,�.fl@;W<aq&3V0f,�n*;60f,i;60*5Q,�qfq�.fl@,�qf36n,6wGP�laO7u�l�0t,�Åa,�uv.fq&.fl@,ip¯36uv.&.fla3V.&.fl@,��936q/AWn*ma./;6.fO�u^�g�3V0tO�36>auv,�qR;6p«.fl@;Iq/,4,�q/.fO7nk3V./;60tqe3V0f,D.fl@,Dqf36n*,6CR 4g6,�0�36575�w=hT;6.fl"ª4��H 36>a<"E&�2�d.�ma0f;�g=O�<@,4uv;InmT,�.fO7.fOQg6,mT,�0tp|;60tnk36>auv,20t,�573V.fOQg6,4./;�.fla,DErE�n*,�.fl@;W<}C�~)l@,D573V0fs6,�0)d ª:)�$���gV3657x@,�q�p¯;60�.fl@,���H n*,�.fl@;W<i3V0f,�<ax@,./;�OQ.fqR573V0fs6,�0Rh?O736qz36>a<m�;=;60zh�;Ixa>?<a3V0fA�,vJT,�uv.�CU~�l@,2573V0ts6,�gV3V0tO73V.fOQ;I>k;6p�.fl@,4d ª8)8$ýp¯;60�E&�2� � O7qz./;�h�,,v¡=m�,�uv./,�<"qfO7>auv,4OQ.Ula36qR573V0fs6,�0�36q/AWn*ma./;6.fO7u�g�3V0tO�36>auv,�.fla36>Z.fl@,2;6.fl@,�0�,�q/.fO7n3V./;60tq�Ce�N�W,�,4:�,�n3V0f� � 36>a<�=,�uv.fOQ;I> � C � C7�O7>ïùa36>�36>a<��DO �/h�,�57q����6�6ú=C ���2;6./,.fla3V.�O7.fq2h�O736qDPz;Ix?57<�hT,&qfn365�5Q,�0D.fla36>ï.fla3V.�;6pR.fl@,;6.fl@,�0tq)OQpr3&h?36>a<@P�O�<@.flk;6p-qfO�É�,�¿ � 8?�Q�4Pz,�0t,�xaq/,�<}CGù@;60�.fl@,�qf36n*m?57,4qfO�É�,�xaq/,�<iO7>i;Ix@0)qfO�n�xa5�3V.fOQ;I>}wW36>a<36>a365Q;6s6;Ixaqf57A*./;&57;=u�365�m�;I5QA=>a;InO7365@0f,�s60t,�qfqfOQ;I>}wW5Q;Wu�365�57;6sIO7q/.fO7u2n*,�.fl@;W<aqUP2OQ.fl0q/§o.�3V0f,�>@;6.�3Vmam�,�3657O7>@sp|;60),�qf.fO7n3V.fO7>@s*.fla,�uv;I>a<aOQ.fO7;I>a365�<aO7q/./[email protected];I>Zp¯x?>auv.fOQ;I>�OQ.fq/,�57pyC

ù@;60),�36u�l';6pS.V�6�*0t36>a<@;Inñqt36n*m?5Q,�q�;6p-qfO�É�, ¿(�#úV�6�WwaPR,�,�q/.fO7nk3V./,�<Ä@G� õ B ����x?qfO7>@s�.fl@,�h?36>a<aP�O7<@.fl�¥«������qf,�5Q,�uv./,�<ÿh=A�.fl@,�h�;=;6.fq/./0t3Vmÿqfutla,�n*,�p|;60=� �ps)� õ �=wR�WC7�'36>a<ý�WC� jCÿ~«;ï.flaO7q&,�>?<}wGPR,"�?././,�< 3m?3V0t36n*,�./0tO�u�n;=<@,�5-p¯;60�ð��R36q�3imT;I57A=>@;InkO7365«O7>�ò=��C���>�.fl@,�.V�6�i0f,�m?57O7u�3V.fO7;I>aq4.fl@,&;60t<@,�0�<@,�./,�0tnO�>@,�<hjA�ª2�/B PR36q�365QP�3�AWq � CiH�,"0f,�m?57O7u�3V./,�<�hT;=;6.fq/./0t3Vm�0f,�qf36n*m�57O7>@s��I�'.fO�n*,�q�CiH�,k;I>a57Aïuv;I>?qfO7<@,�0�la,�0f,.fl@,436<V�/xaqf./,�<"�436<a3V0t3^AI3��cH�3V.fq/;I>�n*,�.fl@;W<Z36>a<".fl@,D5Q;Wu�365�57;6sIO7q/.fO7u2n*,�.fl@;W<ZP2OQ.fl0q1� .=CUùa;60e.fl@,4qt3V�6,;6p�uv;Inm?3V0tO7q/;I>�w�Pz,"u�3657u�xa573V./,�<�.fl@,,�q/.fO7nk3V./,�q�wrp¯;60�.fla,kqf36n*,k<?3V.f3Ww-xaqtO7>@si.fl@,;6ma.fO�n365�h?36>a<aP�O7<@.fl¥�� � ������C�ùa;60-���us�� õ �=wG�WC7�Z36>a<��WC� jwm¥�� � ������P�OQ.fl�.fl@,Zª4�2H n*,�.fl@;W<�O7q��WCF�Iú�.=wU�WCF� � ú�36>a<��WC7���Iú0f,�q/m�,�uv.fOQg6,�5QA6wR36>a<�P�OQ.flý.fl@,�E&�4�d.ïn*,�.fl@;W<ÿO7q*�WCF�I�6ú=wR�WCF�!����36>a<ÿ�WCF�I���ï0f,�qfmT,�uv.fO7g6,�5QA6C�ùÁOQsIxa0f,�.@�93c�ma0f,�q/,�>j.fq�h�;�¡Wm?5Q;6.fq�;6pT.fl@,�<?OKJT,�0t,�>auv,�qÁ;6p�d�ª8)�$UqGh�36q/,�<&;I> �¥r�����-;�g6,�0U.fl@,2d ª8)8$zqGh?36qf,�<*;I>0¥�� � ���}��Cù-O7sIx@0f,�.@�¯h���<?O7q/m?573^A=q�h�;�¡Wm?5Q;6.fq�;6p �¥r���}�Qso¥ � � ���}��O�>�.fl@,iqfO7n�xa573V.fO7;I>�P�OQ.fl�.V�6��0f,�m?57O�u�3V.fOQ;I>aq�C�~�l@,mT,�0tp|;60tnk36>auv,�;6pz,�q/.fO7n3V./,�qDh�36q/,�<�;I> .fla,�h�;=;6.fq/./0t3Vmïh?36>a<aP�O7<@.flaq2O7q4p¯36O70t5QA�uv;I>aqfO7qf./,�>c.�w�365Q.fla;Ix@sIlïO7>n*;Iq/.«u�36q/,�q �¥«���}�T;^g6,�0f,�qf.fO7n3V./,�qS¥�� � ������CÁùÁOQsIx@0f,�qÓ.@�9u^�����¯,��}<a,�m?O7uv.}.�A=m?O7u�365I,v¡W36n*m�5Q,�q};6p=.fl@,G,�q/.fO7nk3V./,�<uv;I>a<aOQ.fOQ;I>?365�<aO7q/./0�[email protected];I>Zp9xa>auv.fOQ;I>aq��@G� õ B ����36>a< Ú@G� õ B �}��C)~)l@,�.�A=m?O7u�365«,v¡W36nm?5Q,�P�36q�qf,�5Q,�uv./,�< O�>'qfxau�l3�P�3�A .fla3V.i.fl@,�uv;60t0f,�q/m�;I>a<aO7>as�d ª:)�$ñP�36q�,��=xa3654./; OQ.fq�n*,�<aO736> O7>�.fl@,�qfO�n�xa5�3V.fOQ;I>üP2OQ.fl .V�6�

Page 12: Methods for Estimating a Conditional Distribution Function ...

0f,�m?57O7u�3V.fO7;I>aq�C���;6./,�.fla3V. Ú@G� õ B �}��O7q)n*;I>a;6./;I>aO7u�36575QA"O7>auv0f,�36qtO7>@s@C

46

810 12 14

X46

810

1214

Y

00.

20.

40.

60.

81

Z

(a) True conditional distribution (m=2)

46

810 12 14

X46

810

1214

Y

00.

20.

40.

60.

81

Z

(b) True conditional distribution (m=3)

0.05

0.06

0.07

0.08

NW LL ANW LG-2

(c) MADEs of estimators (m=2)

0.04

0.05

0.06

0.07

0.08

NW LL ANW LG-2

(d) MADEs of estimators (m=3)

ù-O7sIx@0f, � þD�������0o�� ������w�������� ��������#� �!���#"$%��v.(V���* ����3�: ��+�.-B �;E��C����$7��� ������$���7��q�� ����W4��E ������r�Q�)ð$�5-���Y����ò3�1D ð$�%�kõ��0�*�+�.-���"2 ����,��#46���$7�89��7� �;:��<�=?�*@ A ;�1C\���$7��� ������$��p7��q�� ����W4��E ������1�*��$CS ������>H��Ô@G��ACB �}�������Ç �z.E<1=K4Q@ A ;�)C\���$7��� ������2��P7��+�* ��*��4��E ������)����$CG ������FH�� @G��AIB ����������Ç � � <T=?C�@ A ;��46�G�*"$o�� ���Q��]FLm^_�5�_�����F �;�M`��:7:������O:��bdcF�: ��������*�� ��+�,�� e��=�`[c�@jUV��GC\��#����2�6���F�6�W-��6�*�����������*�� ��+�,�� e�g=�h�h�@GU�:7Ql*�.�� e�673`Fc��*�� ��+�,�� e��=�L#`Fc�@jU�o�SC���do�6-��+�* ���C,�*�� ��+�,�� e�a89�� �;/q"� .>=�hpt5u?v�@38�;���rÇ �P.E<�=?7*@ A ;�46�S��"$��: ��3�Q�V]FLm^_�5�9�����/ �;E�V`a�!7:������O:��bdcF�� ������J�*�� ��+�,�� e�[=�`Fc�@GUP��SC��������2�\�����6�W-:�����\�*�����g�*�� ��+�,�� e�=�h�h�@GU��:7Ql*�0�* e�\7m`Fc����* ����3�: e�V=�L#`Fc�@GUd���$7ao�SC\��{��6-:�q�� ���C_�*�� ��+�,�� e�p89�� �;8q1� .F=�hDt5uKv�@_8�;���-Ç � � <�#��_$�>�Á®¯¥T��Cz1�,�0f,�Pz,�uv;I>aqtO7<@,�0f,�<'36>�ª2:����^��n*;W<@,�5�w

ð � � � õ VúÁð �%� 8 s�� õ . � �Áð M�%� 8 }�� õ � í � ô � � C7�^�P�l@,�0f,D.fl@,D,�0f0f;60�q<í��-Pz,�0f,�O�>a<@,�m�,�>a<@,�>j.UP�O7.fl"uv;Inkn*;I>�<aO7q/./0�[email protected];I>[� * s#� � ô � � +�CGH�,�./0f,�3V./,�<�.yPz;V�36>a<�.fl@0f,�,v��q/./,�m36l@,�36<&m?0f,�<aO7uv.fOQ;I>�w�h=A�.f3V�WO7>@s4ò3�Ó� ð$�%�kõÿp|;60SÇ � .436>a< � CÁù@;60G,�36u�l&;6p��I�6��qf36n*m�5Q,�q;6pGqfO�É�,"¿���úV�6�Ww�Pz,&u�3657u�xa573V./,�.fl@,*d�ª8)�$Uq2P�OQ.fl�36qfA=n*m?./;6.fO7u�36575QAi;6ma.fO7nk365«h?36>?<@P�O7<@.fl?q�;I>�0f,�sIx?573V0

���

Page 13: Methods for Estimating a Conditional Distribution Function ...

0.0

0.02

0.04

0.06

0.08

ANWx=4.99

ANWx=13.71

LG-2x=4.99

LG-2x=13.71

(a) Difference of MADEs

0.0

0.1

0.2

0.3

ANWx=4.99

ANWx=13.71

LG-2x=4.99

LG-2x=13.71

(b) Difference of bandwidths

(c) Conditional distribution

x = 4.99

8.0 8.5 9.0 9.5 10.0 11.0

0.0

0.2

0.4

0.6

0.8

1.0

(d) Conditional distribution

x = 13.71

14.2 14.6 15.0 15.4

0.0

0.2

0.4

0.6

0.8

1.0

ù-O7sIx@0f,1�·þ_�������0o�� ������>�6�*�*�f ��5�����n���.���#"$o�3v.(��*�* ����,�� ����.-[ �;�3 �8 ��ue�� e�?"���;�6�:7�"$�6�67���CS ���Y��'7��q�� ����W4��u �������@G��AIB ���'89�� �;�46�S�� ��� ��Q�*"s46���$7�89��7� �;:��<J=?��@ A ;�M46�G�*"$o�� ��B���' �;�3]FLm^_�5�'46�z�S�67r��� �¥r�����'���+�{�.� �;�,]FLm^_�5�'46�z�S�67r����¥{� � ������<�=Q4K@ A ;�F46�S��"$��: ��B�Q� �¥-�����Ès�¥{� � ������<g=KCQ@w� =K7*@ A ;�MCS���Y��*�,�6�?"$u���������$ ��+�.->C\���$7��� ������$��D7��+�* ��*�W4��E ������[����$CG ������E�"@G� õ B ����(1 �;!��C�~Ff�+���M� @G� õ B ���\UV �;!���gf�+�2�M� �:7Ql*�.�� e�67`a�:7!���Q��O��:bdcF�� ������g���* ����,�� e�*U57!�z�\;�\7Bf�+�2�3��o�SC����o�6-��+�* ���C'���* ����3�: e��=�q"� .j@�<

�6�

Page 14: Methods for Estimating a Conditional Distribution Function ...

s60tO7<�m�;IO7>c.fq�P�O7.fl�q/./,�m��WC��I��O7>�.fl@,��a��<aOQ0t,�uv.fOQ;I>ý36>a<ýq/./,�m?q*�WC7����36>a<ý�WC7����O�>�.fla,�Aj��<aOQ0t,�uv.fOQ;I>}w�p¯;60Ç �z."36>a< � 0t,�q/m�,�uv.fOQg6,�5QA6C���;6./,*.fl?3V.4.fla,&uv;I>?<aOQ.fOQ;I>a365r<aO7q/./0�[email protected];I>?q)uv;I>auv,�0t>@,�<ï>@;�5Q;I>as6,�0D36<?nOQ.qfO7n*m?57,4,v¡Wm?57O�u�OQ.�p|;60tnkq�CU��>�;60t<@,�0�./;Zu�3657u�xa5�3V./,E¥�� � ������w�Pz,�,�g�365�xa3V./,�<'.fl@,�./0tx@,�gV3657x@,�qe;6pS@G��AIB ���)36>a<OQ.fqr<a,�0tOQgV3V.fOQg6,�q«h=A�qfO�n�xa5�3V.fOQ;I>}wV36qrp¯;I575Q;�P�q�CrH�,Rs6,�>a,�0t3V./,�<��V�WwF�6�6�D0t36>a<@;In�qf36n*m�5Q,�q«h=A�OQ./,�0�3V.fO7>@s�� � C7�^�.�PR;i�¯;60R.fl@0f,�,���.fO7n*,�qUqf.f3V0f.fO7>@s�3V.�3��a¡=,�<*gV3657x@,x�«CG~)l@,�0f,�573V.fOQg6,)p¯0f,��=x@,�>auvA*;6p�.fl@,4qf36n*m?5Q,�,v¡Wuv,�,�<aO�>@sA�PR36q�0f,�sI3V0t<a,�<�36q�.fl@,Z./0tx@,"g�3657xa,;6px@G��AIB ����Cï~)l@,0f,�qtxa5Q.fO7>@s uv;I>a<aOQ.fOQ;I>?365U<aO7qf./[email protected];I> p9xa>auv.fO7;I>aq3V0f,�m?5Q;6././,�<'O�>�ù-O7sIx@0f,�q � �93c��36>a<��¯hT��CGH�,�xaqf,�<i�6,�0t>@,�5}n*,�.fl@;W<aqe./;*,�qf.fO7n3V./,�.fl@,�nk3V0fsIO7>a365}<@,�>?qfOQ.�Ap¯xa>?uv.fOQ;I>ïP�OQ.flï3�qf36n*m�5Q,&;6pRqfO�É�,'���6�WwF�6�6�WCZùÁOQsIx@0f,�q � �9u^��36>a< �9<��43V0f,.fla,*hT;^¡=m�5Q;6.fqD;6p�d ª8)8$zq�p¯;60.fl@,x�I�6��0f,�m?57O7u�3V.fO7;I>aq�C��WO7nO75�3V0-./;-$�¡@36n*m?5Q,��Vwch�;6.flkª4��H 36>?<kE&�4�d.�n*,�.fl@;W<aq�m?0f;^gWO7<@,�uv;InmT,�.fO7.fOQg6,mT,�0tp|;60tnk36>auv,D0f,�573V.fOQg6,D./;*.fl@,�ErE�n*,�.fl@;W<}w@O7>"./,�0tnq�;6p-.fl@,�3Vh?q/;I57xa./,4,�0t0f;60e;6pr,�qf.fO7n3V.fOQ;I>}þWP�l?O75Q,4.fl@,h?O736q�;6pÁ.fl@,��2H ,�qf.fO7n3V./;602O�qe0f,�573V.fOQg6,�57AZ573V0fs6,�0^C

ù@;60�,�36utl�;6p.V�6�40t36>?<@;In{qt36n*m?5Q,�qr;6p?qfO�É�,È¿'�#úV�6�WwIPR,z,�qf.fO7n3V./,�<�.fl@,R.�PR;V��q/./,�mk36l@,�36<�ma0f,�<?O7uv.fOQg6,<aO7q/./[email protected];I>�@G� õ B �}��xaqtO7>@s'.fl@,Zh?36>a<@P2O7<@.fl �¥r������q/,�5Q,�uv./,�<�hjA�.fla,kh�;j;6.fqf./0t3Vm�qtutl@,�n*,"p¯;60E�o�é� õ �6�36>a< � � C� =�VC ~�l@,'h�;j;6.fqf./0t3Vmü0f,�qt36n*m?57O7>as�P�36q"uv;I>a<axauv./,�<�36qkp¯;I575Q;�P�q�C H�, �a././,�<�3�57O�>@,�3V00y8����^�n*;=<a,�5r./;i.fl@,*;60�OQsIO7>a365-<a3V.f3Ww�36>a<�qf36nm?5Q,�< .fO7n*,*q/,�0tOQ,�q*�¯P�O7.fl�57,�>@s6.fl�úV�6�c�2p|0t;In .fl@,&�a././,�<�n*;W<@,�5�CH�,�0t,�m?57O7u�3V./,�< h�;j;6.fq/./0�3Vm�qf36nm?57O7>@s0�I�Z.fO�n*,�q�C2ª4qDO7>'.fla,�u�36q/,&;6pm$G¡W36nm?5Q,Z�Vw�PR,�uv;I>?qfO7<@,�0f,�< ;I>a5QA.fl@, 36<��fxaq/./,�<��236<?3V0t3�AI3��cH�3V.fq/;I>û,�q/.fO7n3V./;60i36>a< .fla, 5Q;Wu�365�5Q;6sIO�q/.fO7u�,�q/.fO�n3V./;60ZP2OQ.fl�q��p.=C#H�,uv;In*m?3V0f,�<ÿ.fla,',�q/.fO7n3V./,�qkP�OQ.flý.fl@;Iqf,�h?36q/,�<ÿ;I>ÿ.fla,';6ma.fO7n365�h�36>a<@P�O7<a.fl�¥ � � ������wRP�laO7u�lÿO7q&,��jx?365./;��WC7����.�p¯;60/���J� õ �6�ï36>a<��WCV.W��ú p|;60/�o��� � õ =�"O�>�.fl@,iu�36q/,";6p).fl@,iª2�2H ,�qf.fO7n3V./,6wG36>a<�,��jx?365./;��WCV.��a�p¯;601��� � õ �6�'36>?<��WC7��ú6��p¯;601��� � � õ =�kO�>ï.fl@,ku�36q/,;6p�.fl@,E��2�d.i,�q/.fO�n3V./,6CZùÁOQsIx@0t,-�?�93c�ma0f,�q/,�>j.fq�h�;�¡Wm?5Q;6.fq�;6pT.fl@,�<?OKJT,�0t,�>auv,�qÁ;6p�d�ª8)�$UqGh�36q/,�<&;I> �¥r�����-;�g6,�0U.fl@,2d ª8)8$zqGh?36qf,�<*;I>0¥�� � ���}��Cù-O7sIx@0f,<�?�¯hT��<aO7q/m?5�3�AWq�h�;�¡Wm?5Q;6.fq�;6p �¥r�����·s�¥ � � ���}��O7>*.fla,�qfO7n�xa573V.fOQ;I>&P2OQ.fl0.V�6��0f,�m?57O7u�3V.fO7;I>aq�C��@O7>auv,ePR,xaq/,�<�3ZqfO7n*m�5Q,�57O7>@,�3V04n*;=<a,�5}./;k�a.2.fl@,�>a;I>a57O7>@,�3V0)qf./0txauv.fx@0f,6wTOQ.�O7q2>@;6.2qtx@0fma0tO�qfO7>@s�.fla3V. �¥r�����)365QPR3^A=q;^g6,�0f,�q/.fO�n3V./,�qm¥�� � ���}��CS�Rxa.r.fl@,�,�q/.fO�n3V./,�qÁp|;60S@G��AIB ���«0f,�n36O�>�0t,�36q/;I>a3Vh?5QA�0f,�57O73Vh?57,6C«ùÁOQsIx@0f,È�?�9u^���Z�9<��<@,�m?O7uv.fq�.�A=m?O7u�365r,v¡W36n*m�5Q,�q);6p�.fl@,�,�q/.fO7n3V./,�<�uv;I>a<aO7.fOQ;I>a365«<?O7q/./0tOQh�[email protected];I>"p¯x?>auv.fOQ;I>aqr�@G� õ B �}�)36>?< Ú@G� õ B �}��C~)l@,&.�A=m?O7u�365Á,v¡@36n*m?5Q,*P�36q�q/,�57,�uv./,�<�O7>ïqfxau�l�3iPR3^A�.fl?3V.�.fl@,uv;60f0f,�q/m�;I>a<?O7>@s�d�ª8)�$ûP�36q�,��jx?365Á./;OQ.fq)n*,�<aO�36>�O7>i.fl@,�qfO�n�xa5�3V.fOQ;I>"P�OQ.flÄ.V�6�0t,�m?57O7u�3V.fOQ;I>?q�Cå�XªW �r]Ccfi�cfe!Ímn�Ðôç(aNe�l��r]CÕm]6n�aN]CÕz_¤Ð�Õ��n�]Öe�]ù-O�>a36575QA*PR,�O75757xaqf./0t3V./,);Ix@0)n*,�.fla;=<"P�OQ.flZ.fl@,�B�36>a36<?O736>Z57A=>W¡k<?3V.f3'�¯;I>"3&>a3V.fxa0t365�5Q;6sI3V0tOQ.flankO7u�qfu�3657,��p|;60D.fl@,&A6,�3V0tq*����.W�Ê�t��� � �@C&~)l@,�.fO7n*,&q/,�0tOQ,�qD<a3V.f3"m?57;6.4O7q2ma0f,�qf,�>c./,�<ïO7>�ùÁOQsIx@0f,=�@�93c��C�H�,*,�q/.fO7nk3V./,�<

�².

Page 15: Methods for Estimating a Conditional Distribution Function ...

.fl@,�uv;I>?<aOQ.fOQ;I>a365r<aO7q/./0�[email protected];I>i;6pzð{�zsIOQg6,�> ð$�%� 8 hjA�.fl@,&36<��fxaq/./,�<��236<?3V0t3�AI3��cH�3V.fq/;I>�n*,�.fl@;W<}C2~�l@,h?36>a<@P�O�<@.flaqRPz,�0t,�q/,�5Q,�uv./,�< h=A�.fl@,�h�;j;6.fqf./0t3Vm qfu�l@,�n*,�h?36q/,�< ;I>'0f,�qf36nm?57O7>@s&.fl@,�P�l@;I5Q,�.fO�n*,�q/,�0�OQ,�qp|0f;In .fl@,*h�,�q/.4�a././,�<�57O�>@,�3V08y8����^�4n*;W<@,�5�C�H�,<?O7<'�I�i0t,�m?57O7u�3V.fOQ;I>?q2O7> .fl@,*h�;=;6.fq/./0t3Vmï0f,�qf36n*m�57O7>@sq/./,�m�CU~)la,�,�q/.fO7n3V./,�<'uv;I>?<aOQ.fOQ;I>a365}<?O7q/./0tOQh�[email protected];I>Zp¯xa>?uv.fOQ;I>�O7qe<@,�m?O�uv./,�<'O7>�ùÁOQsIx@0f,"�@�¯h���C

••

••

••

••

•••

••

••

•••

•••

••

•••

••

••

•••

••

••

••

••

•••••

•••

••

•••

••

(a) Lynx data

0 20 40 60 80 100

4

5

6

7

8

9

4

5

6

78

X4

56

78

Y

00.

20.4

0.6

0.8

1Z

(b) Conditional distribution

ù-O7sIx@0f,<�àþm=K�*@)�9���$�!7������M�O��.�37:�: W�:</=K4K@m���* ����,�� e�67�C\���$7��� ������2���7��q�� ����W4��E ������3H-�¼@G��AIB ���#�Q�Gð$�}-���Y����ð �%� 8 ����<

ª2qe36>�3657./,�0t>a3V.fOQg6,�3Vmam?5�O7u�3V.fOQ;I>}wjPz,�uv;I>aqf./0txauv./,�<i.fl@,Dma0f,�<?O7uv.fOQg6,DO7>c./,�0tg�365 * @ � 8^���&{¦.kB �}��w@ � 8^���Ès�&{¦.kB �}�U+zp¯;60a� � �9� ô �^��wrh?36q/,�<ï;I>ï.fl@,*,�q/.fO�n3V./,�<�uv;I>a<aO7.fOQ;I>a365-<aO7q/./[email protected];I>�p¯xa>?uv.fOQ;I>}C�~r;'utl@,�ut�ï;I>mT,�0tp|;60tnk36>auv,6w�PR,kxaq/,�<ï.fl@,<?3V.f3�p|;60Z����.W�Ê�t����.��ÿ�%TU�V���/¿�� ���¦�j�D./;�,�q/.fO7n3V./,0@G��AIB ����w-36>a<�.fl@,5�36q/.����<?3V.f3&mT;IO�>c.fqz./;utl@,�ut�Z.fla,4m?0f,�<aO7uv./,�<Zg�365�x@,�q�CG~)laO�qG.fO7n*,DPR,�xaq/,�<".fl@,D5Q;=u�365�5Q;6sIO�q/.fO7u4n*,�.fl@;W<ZP2OQ.flqr�z.=C�~)la,�0f,�qtxa5Q.fq4P�OQ.flw��� � õ �&3V0f,*0f,�m�;60f./,�<ïO7>�~-3Vh?5Q,��VC�ª4575-.fl@,&ma0f,�<aO7uv.fO7g6,�O7>j./,�0fgV3657qDuv;I>c.f36O�>.fl@,uv;60f0f,�q/m�;I>a<?O7>@s"./0tx@,*gV3657x@,�q�C*~)l@,3^g6,�0t3Vs6,Z57,�>@s6.fl�;6pR.fl@,O7>j./,�0fg�365�q�O7q".=CÆ�V�Ww-P�laO7u�l�O�q1� � CÆ�:  ;6p.fl@,�<@AW>a36nO7u40t36>as6,�;6p-.fla,�<a3V.f3WC

H�,e3657q/;2O�>au�57xa<@,GO�>�~-3Vh?5Q,2�z.fl@,zma0f,�<aO7uv.fO7g6,zO7>j./,�0fgV3657q�h?36qf,�<�;I>�.fl@,R,�q/.fO7n3V./,�<�uv;I>a<aOQ.fO7;I>a365c<aO�q/./0tOK�[email protected];I>�;6p�ð{��sIOQg6,�>*h�;6.fl*ð$�%� 8 36>a<*ð$�%� M C�~r;�;6ha.f36O7>*.fla,�q/,e0f,�qfxa57.fqÁPz,)xaqf,�<&.fl@,)5Q;Wu�365��957O7>@,�3V0Ê�r5Q;6sIO�q/.fO7un*,�.fl@;W< ./;�,�qf.fO7n3V./,�@G��AIB � 8�ô � M ��C�~«;i.flaO7q4,�>a<�w�57,�.�t4��� 8�ô � MVôwv �<�zy&��� 8�ô � MVôwv �|{cóc�<}�y&��� 8�ô � MVôwv �t÷P�OQ.flÄy&��� 8 ô � M ôwv ��� ,v¡Wmr� v Ü } v 8 � 8 } v M � M ��C�~)l@,�,�qf.fO7n3V./;602O�q)<@,��?>@,�<�36qr�@G��AIB � 8 ô � M ��D¼t2�9� ô � ô �v ��wP�l@,�0f, �v <@,�>a;6./,�q).fl@,�nkO7>aO7nO�q/,�0z;6pö �°¡ X ó�L��9ð$� H A@�Ss�t2�9ð$�%� 8 sh� 8�ô ð$�%� M s�� M�ôwv �t÷ MC¢¢¡ ð �%� 8 s�� 8¥ 8 ô

ð �%� M s�� M¥ M £ ô¢ O7qG3�qfA=nn,�./0tO7u�ma0f;6h�3Vh?O757OQ.yA�<@,�>?qfOQ.�A&;I>r��M�w=36>a<r¥ 8 36>a<0¥ M 3V0f,2h?36>a<@P�O�<@.flaq�C���>;Ixa0Uu�3657u�xa573V.fO7;I>}w� �

Page 16: Methods for Estimating a Conditional Distribution Function ...

Pz,"qfO7n*m?57A�u�l@;Iq/, ¢ ./;�h�,.fl@,"q/.f36>a<a3V0t<��D36xaqfqtO736>��6,�0t>a,�5U36>a<�¥ 8 �G¥ M C�~)l@,Zh?36>a<@P�O�<@.flaq4Pz,�0t,q/,�5Q,�uv./,�<�h=A�.fl@,*h�;j;6.fq/./0�3Vm�qfutla,�n*,h?36q/,�<ï;I>�0f,�qf36n*m?5�O7>@s".fO7n*,q/,�0tO7,�q�p|0t;In .fl@,h�,�q/.D�a././,�<�5�O7>@,�3V0y:��¤.I�Án;=<@,�5�CÁ Dx@.Á;6pÁ���Dma0f,�<aO�uv.fOQg6,eO7>c./,�0tg�3657q�w6;I>a5QA�;I>@,��¯p¯;60G.fl@,�A6,�3V04����.6�I�ÁnO7qfqf,�<�.fla,e./0tx@,�g�365�x@,6w36>a<�.fl@,�>ï;I>a5QA'>a3V0t0f;^P�57A6C�~)l@,&3�g6,�0t3Vs6,Z5Q,�>@s6.fl�;6pU.fl@,*O7>j./,�0fgV3657qDO7qD>@;^P 0t,�<axauv,�<�./;��VCÆú � w�P�laO7u�lïO7q� .=CÆ�: ñ;6p-.fl@,�<@AW>a36nO�u20�36>@s6,�;6p-.fl@,�<a3V.f3WC~r3Vh?57,�¦þz+G0t,�<aO7uv.fOQg6,�O7>j./,�0fgV3657qep¯;60DB�36>?36<aO736>�5QAW>W¡�O7>�����.����t��� � �@w}h?36q/,�<�;I>�.fl@,�<a3V.f3kO7>�����.W�Ê�t����.��@C~)l@,�>@;InO�>a365�uv;^g6,�0t3Vs6,&ma0f;6h�3Vh?O757OQ.yAkO7qe�WCÆ�=C

¤d¥�¦G§ ¨$§?©:¥�ª�¦S«f©:¥ ¬ §?¥*­�®f¯6°?±j§$²%§K±G³J±G´:¥«�¦SµjµG¥�­pª�¦S«f©:¥ ¶·{¸q¹0º ¬ §?¥*­�®f¯6°?±j§�²%§?±j³g°W»i±«�¦SµjµG¥�­#ª�¦S«f©:¥�¼ ¶·{¸q¹½S¾e¹0¿*ºÀ�ÁzÂGà Ä:ÅfÀ�Ä Æ Ã:Å ÄjÁ:Ç:Ä:Å ÈGÁSÉ Ê:ÅfÀ*ÂGË Æ È:Å ÄGÈ!Ç:Ä:Å ÈGÊ�É Ê:ÅÌÂ�Í�ÃÀ�ÁzÂSÈ Î�Å ÁGÄ Æ Ã:Å ÁjÁ:Ç:Ä:Å Ä:À\É Ê:Å ËSÍzÊ Æ È:Å ÄGÈ!Ç:Ä:Å Ä:À6É Ê:ÅÌÃjÎSÊÀ�ÁzÂjÎ Î�Å ËSÍ Æ Ã:Å ÁGÍ!Ç:Ä:ÅÏÎSÃ�É Ê:Å ÍjÄzÃ Æ È:Å ÍjÊ!Ç:Ä:ÅÌÂSÈ�É Ê:ÅÏÎ�À�ÃÀ�ÁzÂSÄ È:ÅÌÂjÎ Æ Ã:Å ÍzË:Ç:Ä:Å ËjÃ�É Ê:ÅfÀ�ÁzÃ Æ Ã�Å ÍGÍ.Ç:È:Å ÄGÈ�É Ê:ÅÏÎ�À�ÃÀ�ÁzÂSÁ È:ÅfÀ�Ä Æ Í.Å ÈjÁ:Ç.Î�ÅÏÎ�À\É Ê:ÅÌÂSÈjÄ Æ Í!Å ÈGÊ!Ç:È:ÅfÀ�È�É ÀGÅ ÊGÁzÃÀ�ÁjËGÊ È:ÅÌÃSÊ Æ Í.Å ÈzÃ�Ç.Î�ÅÏÎ�ÊSÉ Ê:Å ËSÍzÊ Æ Ã�Å ÍjË!Ç.Î�Å ÊGË�É Ê:Å ÄGÈjÊÀ�ÁjË:À È:Å Á:À Æ Ã:Å Â:ÀGÇ.Î�ÅÏÎSÂ�É Ê:ÅÌÂSÈjÄ Æ Ã�ÅÏÎ�ÀjÇ.Î�ÅÌÃSÊ�É Ê:Å ÄGÈjÊÀ�ÁjËj Î�Å ËzÎ Æ Ã:Å Ë�Î�Ç.Î�Å ÄjÂ�É Ê:ÅÌÂSÈjÄ Æ È:Å ËGÄ!Ç:Ä:ÅfÀ*Â�É Ê:Å ÄGÈjÊÀ�ÁjËGË Î�Å ÄGÄ Æ Ã:Å ÍjÍ!Ç:Ä:Å ËGÄSÉ Ê:ÅfÀ*ÂGË ÆÌÎ�ÅfÀ�Î�Ç:Ä:ÅÌÂGÃ�É Ê:ÅÏÎ�À�ÃÀ�ÁjËSÍ Ä:ÅfÀ�Ë Æ Ã:Å ÄjÁ:Ç:Ä:ÅÏÎ�ÍGÉ Ê:Å ÍjÄzà ÆÌÎ�ÅÌÂSÈ!Ç:Ä:Å Ä:À6É ÀGÅÌÂSÊzÃ

Ð Ñ 5/4Gê�éC4�è�îfíSú<7Àû&é}ê:û�4GéTè}îw4�üù@;60�.fl@,�5Q;=u�365}57;6sIO7q/.fO7uD,�q/.fO�n3V./;60��@G��AIB ���RPR,�;I>a5QA"uv;I>aqfO7<a,�0)p¯x?>auv.fOQ;I>aqQy�;6pr,v¡Wm�;I>@,�>j.fO7365K��m�;I5QAW>@;InO7365.�A=mT,6wWP�O7.fl0q=×o.àþ�y&��� ôwv �m� ,v¡=m-� vI8 � Ü } õ�õ�õ } v � � � � 8���CUE«,�.kÒ�<@,�>@;6./,D.fl@,�n3V0fsIO�>a365�<a,�>aqfOQ.yA;6p�ò=��CH�,�O7n*m�;Iq/,D.fl@,�p¯;I575Q;�P�O7>@s&0f,�sIx?573V0tOQ.yA"uv;I>a<?OQ.fOQ;I>aq�þ

��BD�^�iù@;60'�a¡=,�<jA�36>a<j�«w_Ò�������§��Ww4��Ó�@G��ACB �}�rÓ �Vw_Ò{O7q"uv;I>c.fO�>jx@;Ix?q"3V.��rw236>a<@G��AIB�~ ��l?36q8. * ��q8}û�^�|{¦.f+Guv;I>c.fO7>=x@;Ixaq4<@,�0tO7g�3V.fOQg6,�q4O7> 3k>@,�OQsIljh�;Ix@0tl@;=;W<�;6pS�«wTP�l@,�0f,* Ô +r<@,�>@;6./,�q�.fl@,�O7>j./,�s6,�0�m?3V0f.e;6p Ô C��B½.I�i~)l@,��6,�0t>@,�5 ¢ O�q23"q/AWnn*,�./0tO7uVw�uv;In*m?36uv.f57A qfx@m?mT;60t./,�<'ma0f;6h�3Vh?O757OQ.yA"<a,�>aqfOQ.yA�qf3V.fO7q��

p¯A=O7>as(B ¢ ��� 8 ��s ¢ ��� M ��B HJÕ B � 8 s�� M Bjp|;60<� 8�ô � M C��B � �i~)l@,�m?0f;=uv,�qtqDój�¯ò=� ô ð����t÷�O7qe3Vh�q/;I57x@./,�5QA"0f,�sIxa5�3V0�w·TN�V���Ö �o×j��D qfx@m��Ø 8 MBÙ qtx@mÚdÛjÜ�ÝÞ�ßjà B Fk�%y=B á �8 ��s�FZ�%yD��Boâr� � 36qã×-� Á ô

� �

Page 17: Methods for Estimating a Conditional Distribution Function ...

P�l@,�0t,�á ã� <@,�>@;6./,�q�.fl@,0ìT���a,�5�<�s6,�>@,�0t3V./,�<�hjA�ój�¯ò�ë ô ðëV�Eþ�¾ H ï H ×@÷IC"ù[email protected]@,�0�wØ ã Ø 8 ×IM Ö �o×j�KäQ�­��8 � ä �pÓ Á p¯;60Dq/;In*,/å � * � ô �^��C&�¯H�,�<a,��?>@,"ê0æÈ� �kP2l@,�>Äêr��ç:��WC �

��BÈ�j�iª4q<¿'� Á w�¥�� �36>?<�57O7nÿO7>@p�ö�èVé�¿b¥aM � § �WC�Z¥��_?]jêë�{ìZí8T°¯ « ¶�¯w¯wT ©�¸ ©zîr«,©�¸6³ TN±¤T ©�¸ ¯²� ª4qfqfxan*m?.fOQ;I> ��B � �"l@;I57<aqiP2OQ.flså�� �üOQp�36>a< ;I>?5QA�OQp.fl@, m?0f;=uv,�qtq�ój�¯ò=� ô ð���t÷�O�q0Çi��<@,�m�,�>a<a,�>c.Zp|;60�q/;In*,hÇ × �VC ~)l@, 0f,��jx?OQ0f,�n*,�>j."O�>���B½.I�k.fla3V. ¢hT,uv;Inm?36uv.f5QA�qfx@mam�;60f./,�<ïO7q�O�n*m�;Iq/,�<ïp|;60�.fl@,kqf3V�6,;6p�ha0t,�g=OQ.yA�;6p�ma0f;=;6p9q�w«36>a<�u�36>�hT,*0t,�n*;^g6,�<�3V..fl@,"uv;Iqf.�;6p�57,�>@s6.flaOQ,�0�3V0fsIxan*,�>j.fq�C���>�m?3V0f.fO7u�xa5�3V0�w«.fl@,Ä�D36xaqtqfO736>��6,�0t>@,�5RO7q�365757;^PR,�<}C���> ��B � ��w�.fl@,36qfqfxan*m?.fOQ;I>*;I>Z.fl@,�uv;I>jg6,�0fs6,�>auv,D0t3V./,4;6p Ö �o×j�UO7qU3657qf;�>@;6.G.fla,�PR,�3V�6,�q/.�mT;IqtqfOQh?5Q,6C-~)l@,�5�36q/.Uuv;I>a<aO7.fOQ;I>O7>���BQ�j�)n3^A�h�,�0t,�573�¡=,�<�OQp�PR,�3V0t,�m?0f,�m?3V0f,�<�./;iqf./0f,�>@s6.fl@,�>ÿ��B � ��q/;In*,�P�l?3V.�CDùa;60�,v¡W36n*m�5Q,6wTO7p�.fl@,ma0f;Wuv,�qfq)ój�¯ò=� ô ð���t÷�O�q�Çi��<@,�m�,�>a<@,�>j.U.fla,�>}wjp¯;60e~)l@,�;60f,�n �2h�,�5Q;^P�wjPz,�>@,�,�<Z;I>a5QA=¿b¥�� Á w@>@;6.È¿b¥ M �hT;Ix?>a<@,�<�3�P�3�Aïp|0t;In �WC�1�;�Pz,�g6,�0^wrqfO7>?uv,i��BÈ�j�4O�q43657PR3^A=q�qf3V.fO�q/�a,�<�hjA h?36>a<@P2O7<@.flaq�;6pU;6ma.fO7nk365-qtO�É�,�%TN�V���m¥Bï uv;I>aq/. õ ¿ � 8?�­�KM � � 8d����waPR,�qfla36575}>a;6.�uv;I>auv,�0t>�;Ixa0tq/,�5Qg6,�qeP2OQ.fl�qfxau�l�0f,��?>@,�n,�>c.fq�C�Z¥��_?]jê��ðì[ñ ©�¸ ¯wT�¯²±U� ¸C«Qò �&�y.�nk3�Aïh�,�m?0f;^g6,�<�.fla3V.�wrxa>?<@,�0�uv;I>a<aOQ.fO7;I>aq*��BD�^���T��BÈ�j��36>a<�36qfqfxankO7>@sq/×j.=w �v ��� � v Ü O7>ima0f;6h�3Vh?O757OQ.yA6wWP�l@,�0f, v Ü � v Ü��� O7q)x?>aO7�=x@,�5QAk<@,���>@,�<ihjA@ � � � ��AIB ���m�¼t � � � �9� ôwv Ü � ô ¾�� � ô � ô�õ�õ�õ�ô q s � ô ���@C7�^�36>a<0@&� � �fwàt<� � �-3V0f,236qRO7>r�W,�uv.fOQ;I>�.=C7�VC���.Up¯;I575Q;�P�qGp¯0f;Ino.flaO7qG0t,�qfxa5Q.G.fl?3V.z3V.È�«w��@G��AIB�~ �U36>a<kOQ.fqU�a0tq/.mq�sï�<@,�0tOQgV3V.fOQg6,�qe3V0f,�uv;I>aqtO7q/./,�>j.Rp¯;60e.fl@,�uv;60f0t,�q/m�;I>a<aO7>@s�<@,�0tOQgV3V.fOQg6,�q�;6p�@G��ACB�~ ��CU��>i.fl@,�u�36q/,�;6p«.fl@,&ø É�,�0f;6.fl<@,�0tOQgV3V.fOQg6,6wQ£@~)l@,�;60f,�n �2P�O7575?,v¡=./,�>?<Z.fl?O7qUm?0f;6m�,�0f.�A./;*3�<@,�.f36O75Q,�<i<@,�qtuv0tOQma.fOQ;I>k;6p�.fl@,�q/./;Wutla36qf.fO7uD36>a<q/A=qf./,�n3V.fO7u�,�0f0t;60tqe;6p1�@G��ACB�~ ��C)4,��?>@,[ó ã �Nô � ã ¢ �����à>®��36>a<gõ ã �Nô � ã ¢ ������MC>®�«C�E�,�.'ö�<@,�>@;6./,i.fl@,�qM÷�q�n3V./0tOK¡�P2OQ.fl��¾ ô ×j��£Â.fl�,�5Q,�n*,�>j.aó·��� ã � M wr36>a<>óC� � L ã �eh�,&.fl@, ��¾ ô ×=��£Â.fl�,�5Q,�n,�>c.�;6ppö � 8�CkE«,�.1q 8 � . * ��q }{�^�|{¦.f+e36>a<[email protected]ø���AIB ����Mx�¼@G��AIB ���?óc�:s�@G��ACB �}�t÷�{�Ò�������w

ù � ������� ��q^� � � 8 Ù @ � � ° � ��AIB ���Ss�t � � ° � �9� ôwv Ü � â � ��¡ 8 ó ��8/L � � ó � ° �Ö�ª� 8}ôø M� � ó ¡ � ��¡ 8 ó ��8/L � � � ��� 8 £ M ¢ ���}� M >!� õE�,�.pú�ö 8�ô ú�ö MVô ú�ö X <@,�>@;6./,�0t36>?<@;In g�3V0�O73Vh?5Q,�q�P�O7.fl�.fl@,�q/.f36>a<?3V0t<'�2;60tn365�<aO�q/./0tOQh?xa.fOQ;I>}C~)l@,�;60f,�n �VC4��¾��x�Wxamam�;Iq/,:q=×o.36>a<�uv;I>a<aOQ.fO7;I>aq�� Õ �����T� Õ �=�Rl@;I57<�CG~)l@,�>�36q<¿'� Á w

�@G��AIB ����s�@G��ACB �}��� ��¿b¥�� � 8?��M ø���ACB �}�0ø � ú�ö 8 }�¥ � ° ù � �����C}�� � Ù·¥ � ° }#��¿b¥T� � 8?��M â ô ���@CV.I��²�

Page 18: Methods for Estimating a Conditional Distribution Function ...

��¾N¾���ª4qfqfx?n*,�uv;I>a<aOQ.fO7;I>aq�� Õ �����T� Õ �=�zP�OQ.fl�q"� .=CU~�l@,�>'36q½¿(� Á wÚ@G��AIB ����s�@G��AIB ���m� ��¿b¥�� � 8?��M ø���AIB ���õ 8?��MÜ ú�ö M } 8M ¥ M ó M @ �¸Mw� ��ACB �}�I}�� � Ù^¥ M }#��¿b¥T� � 8?��M â õ ���@C � �~)l@,��a0�q/.&./,�0tn(;I>ÿ.fla,'0tOQsIlj.���la36>a<ÿqfO�<@,�O7>ýh�;6.fl ���@CV.I�*36>a<{���@C � �&0f,�ma0t,�q/,�>c.fqma0f,�<@;InO�>a36>c.f57A

,�0f0f;603Vh�;Ix@.�.fl@,'n*,�36>}wU36>?<ý.fl@,�q/,�uv;I>a<ý./,�0tn 0f,�m?0f,�q/,�>j.fq&ma0f,�<@;InO�>a36>c.f57A�h?O736q�C���.*n3�A�h�,iqf,�,�>p|0f;In .fl@,2.fl@,�;60f,�n .fla3V.R./;��a0�q/.G;60t<@,�0^wj;Ix@0�n*,�.fl@;W<aqU,�>���;�A.fl@,4qf36n*,Duv;I>cg6,�0fs6,�>?uv,�0t3V./,�q�36qU.fl@;Iqf,2;6pSUx�36>a<'�6;I>@,�q������6�6�I��wTxa>a<@,�0eqfO�nO7573V0z0f,�sIxa573V0tO7.�AZuv;I>?<aOQ.fOQ;I>aq�Ce�|SUx�36>?<'�6;I>@,�q�./0f,�3V./,�<';I>a5QA.fl@,�u�36qf,;6pÁO�>a<@,�m�,�>a<@,�>j.R<?3V.f3Ww?l@;^PR,�g6,�0�C �

�Z¥��_?]jêüûðì'ñ © ¹aý ¬ ´­T�¯ ©�¸À©zî �@ ¬¦¸6³#¨ª©·«­¬¦¨ ý ©�¨fòk¸© ¹�T ¬¦¨ �,¯²±¤T�¹ ¬ ± © ´��2~«;"�a0tqf.�;60t<@,�0^wT36>a< p¯;602s6,�>@,�0�365�«w�.fl@,i36q/AWn*ma./;6.fO7uZg�3V0�O736>auv,";6p��@G��ACB �}��O�q�,v¡@36uv.f5QA�36q&O7>�.fl@,iu�36q/,i;6p�5Q;Wu�365Um�;I5QAW>@;InO7365U0f,�s60f,�qfqtOQ;I>,�q/.fO7n3V./;60tqU;6p};60t<@,�0�qWþ=p|;60z.fl@,�573V././,�0^w=q/,�,�p|;60z,v¡W36n*m�5Q,�:�xamam�,�0f.�36>a<H�36>a<������6���j��Cz~)l?O7qGqfO7nkO7573V0tOQ.yA,v¡=./,�>a<?q�3657q/;i./;'.fl@,*h�O736qD./,�0tn�w�./;�.fla,*,v¡=./,�>j.�.fla3V.�p¯;60�h�;6.flô�@ý36>a<�5Q;Wu�365Ám�;I5QAW>@;InO7365r,�q/.fO7n3V./;60�q.fl@,)h?O736qUO7q�;6p�;60t<@,�0Q¥ � p|;60z,�g6,�>0q�36>a<�¥ � � 8Gp¯;60U;W<a<=qWwc36>a<��¯./;�.flaO7qG;60t<@,�0Ê�Á<a;j,�qG>a;6.z<@,�m�,�>a<&;I>k.fl@,<@,�qfOQsI>Z<@,�>aqfOQ.yA,Ò-CÁ12;^PR,�g6,�0�[email protected]@,2p|;60�nqU;6p}h�O736qU36qzp¯x?>auv.fOQ;I>a3657qU;6p}.fl@,�øF0t,�s60f,�qfqfOQ;I>"n*,�36>}£à@�3V0f,D�=xaOQ./,<aOKJ�,�0f,�>c.�CG~�laO7q�O7qe3*uv;I>aq/,��=x@,�>auv,�;6pr.fl@,�p936uv.e.fla3V.�w?x?>a57OQ�6,D3*5Q;Wu�365}m�;I5QA=>a;InO7365�,�q/.fO7n3V./;60�w��@G��AIB ���eO7quv;I>aq/./0t36O7>a,�<�./;k57OQ,DP�O7.flaO7>��9� ô �^��C

�Z¥��_?]jêÿþdìüñ © ¹�ý ¬ ´OT�¯ ©�¸o©zî Ú@ ¬¦¸6³?¨ª©·«­¬¦¨x¨ T ¸ � ¬ ´r�,¯²±¤T�¹ ¬ ± © ´f�ü��.ku�36>�hT,'qtl@;^P�>ü.fla3V.�we36qfqfxankO7>@s��BD�^���T��BÈ�j�zp¯;60Èq"� .=wW.fl@,�36q/AWn*ma./;6.fO�u2p¯;60tn�xa573"���@C � �zp|;60 Ú@G��AIB ���zO7q�qfla3V0f,�<Z,v¡@36uv.f5QAkh=A.fl@,�q/.f36>a<?3V0t<5Q;=u�365«57O7>@,�3V0�,�q/.fO7nk3V./;60��@����r��AIB ����wT<@,�0tOQg6,�<ih=AinO7>aO7nkO7qfO7>@s

ö ��¡ 8 ó�L��9ð ��H A@�&s>�Às Ö �¯ò � s����t÷ MC¢0£ �¯ò � s��}�P�OQ.flD0f,�q/m�,�uv.�./;&��� ô Ö �}36>a<�.f3V�WO7>@s��@����r��AIB �����u��UCÁ��;6./,6w6l@;�Pz,�g6,�0�wV.fla3V.rxa>a57OQ�6, Ú@�wC�@�����O�q�uv;I>aq/./0t36O�>@,�<>@,�OQ.fl@,�0�./;�5�OQ,h�,�.�PR,�,�>ÿ� 36>?<��Z>@;60&./; h�,Zn;I>@;6./;I>@,iO7>�ATC ª4<a<aO7.fOQ;I>a36575QA6w Ú@üO7q�q/;In*,�P2la3V.�n;60f,0f,�qfO7q/.f36>j.D3VsI36O7>aq/.D<a3V.f3iq/m?3V0tqf,�>@,�qfq2.fla36>¼�@ ��� C�ù@;60D,v¡W36n*m�5Q,6w}OQ.2>@,�g6,�0�36qfqtxan*,�q4.fl@,�p|;60tn �9>@;I>·É�,�0t;>jxan�h�,�0Ê���W��É�,�0f;j��C�Z¥��_?]jê���ì�ñ © ¹aý ¬ ´OT�¯ ©�¸'©zî �@ ¬¦¸C³ Ú@S�Á��>'.fl@,�u�36q/,1q"� .=w-���@CV.I��0f,�<ax?uv,�qe./;

�@G��AIB ����s�@G��AIB ���m� ��¿b¥�� � 8?��M ø���AIB ���0ú�ö 8 } 8M ¥ M ó M ù M ��ACB �}�I}�� � Ù ¥ M }#��¿b¥T� � 8?��M â ô ���@C��j�P�l@,�0f, ù M ��AIB �����¼@ �KMw� ��AIB ����s @&��8d�t��AIB ����M�óc�<s�.¦@G��AIB ���t÷@G��AIB ���tóc�xs�@G��ACB �}�t÷36>a<j@ � � � O�qZ<@,���>@,�<ü36qiO7>¼�=,�uv.fOQ;I>¼.=C7�VC BR;Inm?3V0tO7>@s ���@C � �k36>?<����@C��j�kPR,�q/,�,�.fla3V.��@G��ACB �}���¯P2OQ.flq-�P.I��36>a< Ú@U��AIB ���)la3�g6,�.fl@,�qt36n*,�36q/AWn*ma./;6.fO�u�gV3V0tO736>auv,6w�[email protected]@,��a0�q/.���;60t<@,�02h?O736qep¯;60tn�xa573*;6p

��ú

Page 19: Methods for Estimating a Conditional Distribution Function ...

.fl@,p¯;60tn*,�0�uv;I>j.f36O7>aq�36>�36<a<?OQ.fOQ;I>a365-./,�0tn�C"��>�uv;I>aq/,��=x@,�>auv,6wÁOQpQ@G��ACB �}�/Ó 8M .fl@,�>�@G��AIB ����O7q�h?O�36q/,�<<@;^P�>jP�3V0t<aqe0f,�5�3V.fOQg6,�./; Ú@G��AIB ����waP2laO75Q,DOQp�@G��ACB �}�Q§ 8M .fl@,�>'O7.)O7qeh?O736qf,�<�x@mjP�3V0t<aq�C�Z¥��_?]jê�ðìFñ © ¹�ý ¬ ´OT�¯ ©�¸� TU± ��� ¬î³à¬ ´ ¬�òà¬����0¬ ±¤¯ ©�¸ �,¯²±¤T�¹ ¬ ± © ´��&~)l@,*36>a365Q;6sIx@,*;6p����@C � �D36>a< ���@C��j�O7>i.fl@,�u�36q/,�;6p-.fla,��236<a3V0�3�AI3��cH�3V.fq/;I>ï,�q/.fO�n3V./;60�w

�@�������ACB �}��� Ý ö  ��¡ 8 L��9ð� H Aa� ¢0£ �¯ò=�6s���� áCâ¼Ýö  ��¡ 8 ¢r£ �¯ò=�Ish��� á ô

O7q

�@�������AIB ����s�@G��AIB ��������¿b¥�� � 8?��M ø���AIB ���õ 8?��MÜ ú�ö X } 8M ¥ M ó M ù ��AIB ���C}�� � Ù·¥ M } ��¿b¥�� � 8?��M â ôP�l@,�0f, ù ��ACB �}�½�R@&�¸Mw�Ê��ACB �}�b}j.9Ò������ � 8�Ò��������à@&�|8d����AIB ����C��2;6./,*m?3V0f.fO7u�xa5�3V0t5QA".fla3V.�w�xa>a57O7�6,�36>cA ;6p-�@Áw Ú@36>a< �@����«w"�@���� la36q�3 h?O736q�.fl?3V.�<@,�m�,�>a<?q�./;��a0tq/.�;60�<@,�0�;I>�.fl@,"<@,�>aqfO7.�A>Òÿ;6peò=��C�12;^PR,�g6,�0�wz.fl@,g�3V0tO�36>auv,�qe;6p�36575�p¯;Ix@0),�q/.fO7nk3V./;60tq��²�@�P�O7.fl�q1�P.I��3V0f,�O7<a,�>c.fO7u�365�./;k�a0tq/.e;60t<a,�0�C�Z¥��_?]jê��$ì,ñ ©�¸ ±¤T ¸ ¶�TU± òh©zî @G��AIB ��� TN± �'´,�,¯eýS� « ±x± © AÖ�4BR;I>a<aOQ.fO7;I>aq���BD�^���T��BQ�j�)0t,��jxaO70f,�uv;I>j.fO7>jx?OQ.�A;6p�@G��ACB �}��P�OQ.fl�0f,�q/m�,�uv.�;I>?5QAZ./;��«wT>@;6.�./;rA�Ce��>'m?0tO7>au�OQm�5Q,2PR,�uv;Ix?57<',v¡Wm?5Q;IOQ.2qfn*;=;6.fla>@,�qfq�;6p�@G��ACB �}�O7>�AZh=A6wap¯;60),v¡@36n*m?5Q,6wa.f3V�WO7>@s*.fla,�O7>j./,�s60t365�3�g6,�0�3Vs6,�;6p1�@G��~ªB ����;60 Ú@G��~ªB ���eO7>i.fl@,�>@,�O7sIlch�;Ix@0tla;j;W<k;6p�ATw.fl@,�0f,�h=A�;6ha.f36O7>?O7>@s236>&,�qf.fO7n3V./;60�.fla3V.Gla36<�m�;6./,�>j.fO736575QA�57;^PR,�0�g�3V0tO�36>auv,6C-12;^PR,�g6,�0�w=36>cA&O7n*ma0t;^g6,�n*,�>j.O7>"mT,�0tp|;60tnk36>auv,4O�qR3^g�36O�573Vh?5Q,4;I>a5QA./;qf,�uv;I>a<i;60t<@,�0�CG~r;*3Vmama0f,�u�O�3V./,4P2lcA6wa>@;6./,D.fla3V.)O7pIA 8 H A M .fla,�>}w./;��?0tq/.k;60�<@,�0�w�.fla,�uv;�g�3V0tO�36>auv,�;6pÀ�@G��A 8 B ���Z36>a< �@G��A M B ���k,��=xa3657qï��¿b¥�� � 8O@G��A 8 B ���?óc�=s @G��A M B �}�t÷�ø@M� wP�laO7u�l}wj36qQA 8�ô A M ��ATwWuv;I>jg6,�0fs6,�qe./;�.fl@,4�a0tq/.���;60�<@,�0z./,�0�n O�>k.fl@,4gV3V0tO736>auv,4;6p8�@G��AIB ����C���.zp¯;I575Q;�P�qU.fl?3V.>@;�a0tqf.���;60t<@,�0)0f,�<?xauv.fOQ;I>aq)O�>�g�3V0�O736>auv,�3V0f,�;6ha.f36O7>a3Vh�5Q,�hjA�3^g6,�0t3VsIO7>@s";^g6,�0DgV3657x@,�qe;6p"�@U��HB �}��p¯;60#HZO7>3<@,�uv0f,�36qfO�>@sI5QAZqtn36575}>@,�OQsIljh�;Ix@0tl@;=;W<Z;6p&ATCU~)l@,�qf36n*,�3V0fsIxan*,�>j.�3Vmam?5�OQ,�q�./; Ú@ÁC

��nma0f;^g6,�n,�>c.fq'O�>ü.fl@,�uv;I>jg6,�0fs6,�>auv,�0�3V./,ïu�36>?>@;6.�w4O�>�s6,�>a,�0t365�w�h�,�;6ha.f36O7>@,�< ,�g6,�>#h=Aüla3^g=O�>@sm?3V0t36n*,�./0tO�u��=>@;�P�5Q,�<@s6,e;6pC@G��AIB ���Á36qz3�qfn*;=;6.fl*p9xa>auv.fOQ;I>&;6p6ATCÁ~�laO7qÁO7q�m�,�0tla3Vm�q-n;Iq/.Uu�5Q,�3V0t57A�q/,�,�>hjAuv;I>aqfO7<@,�0�O7>@s236>�,v¡@36n*m?5Q,6wI36qÁp¯;I575Q;�P�q�CS�Wx@mam�;Iq/,z.fl@,R<?O7q/./0tOQh�[email protected];I>�;6pÁ�¯ò ô ð�rO7q«�W>@;�P�>�./;4h�,�3DnOK¡W.fx@0f,;6p�.fl@,�<?O7q/./0tOQh�[email protected];I>aqR;6p2�¯ò���8d� ô ð��|8d�y��36>a<��¯ò��¸Mw� ô ð��KMw�y��w�P�l@,�0t,�O7>',�36u�l�u�36q/,�ò�� � ��O7q2O7>a<@,�m�,�>a<a,�>c.e;6pð � � � þ-36>?<�qfx@mam�;Iq/,&.fl@,nOQ¡WO7>as"m?0f;6m�;60f.fOQ;I>ï36>a<�.fl@,<?O7q/./0tOQh�[email protected];I>aq�;6pRò ��8d� w«ð ��8d� 36>a<�ð �KMw� 3V0f,Z36575�=>@;�P�>}Ci~)l@,�>}wrma0f;�g=O7<a,�<�.fl@,knOQ¡WO7>as�ma0f;6m�;60f.fOQ;I>�O7q�>@;6.���;60Z�Vw-ò 36>?<�ð 3V0f,k>@;6.�O7>a<@,�m�,�>a<a,�>c.�w36>a<'@G��AIB ���)O7q)3�W>@;�P�>}w?qfn;j;6.fl�p¯xa>?uv.fOQ;I>a365};6pÁ.fl@,�<@,�>aqfOQ.yA���;6p�ò��¸Mw�/C���.)p¯;I575Q;^P2q).fla3V.2.fl@,�0t3V./,�3V.P�laO7u�l�@G��ACB �}��u�36>�h�,,�q/.fO7n3V./,�< �¯p|;60&36>jA��a¡=,�<�A@��O7q�O7<@,�>j.fO7u�365�./; .fla3V.�P2OQ.fl�P�laO�utl��D������u�36>�h�,,�q/.fO7n3V./,�<}C(è2>a<a,�0�uv;I>a<aO7.fOQ;I>aqZ��B��^���T��BÈ�j��wG.flaO7q�O7q�.fla,Zqf36n*,"36q�.fl@,k0t3V./,iO7n*m�57O7u�OQ.�O7>�~)l@,�;60f,�n �Vw0f,�sI3V0t<a5Q,�qtqU;6p«36>jAqfn*;=;6.fla>@,�qtqU;6pb@G��AIB ���UO7>rA*.fla3V.�nOQsIlj.Uh�,23^g�36O75�3Vh?5Q,�.fla0f;Ix@sIl"36qfqfxan*m?.fOQ;I>aqUnk36<@,3VhT;Ixa.)qfn*;=;6.fla>@,�qfqe;6p-.fl@,�<?O7q/./0tOQh�[email protected];I>aqz;6p-ð0��8d�z36>a<'ð0�¸Mw�fC

��

Page 20: Methods for Estimating a Conditional Distribution Function ...

� � û=û�4Uç&ëî� "!$#�é}ê�ê&%²üH�,�<@,�0�OQg6,�;I>a57A����@CV.I��w�>a;6.fO7>@s.fla3V.D3m?0f;j;6pÁ;6p2���@C � ��O7q2qfO7nO75�3V0)h?x@.�qtO7n*m?5Q,�0^C�ùa;60436>jA(' � �9� ô �^��w}OQ.p|;I5757;^P�q4p¯0f;In :),�n3V0f�h.".fla3V.D.fl@,�0f,&,v¡@O7q/.fq*) � �9� ô Á �4qtxautlï.fla3V. F&ó,+ �vf��� s v Ü + H )�÷�× �:s-'*p¯;6036575rqtx·�ku�OQ,�>j.f5QA'573V0fs6,/¿�C�E�,�."Æ � Æ*�.)@�4<a,�>@;6./,&.fl@,�u�57;Iq/,�<ïh?36575ruv,�>c./0f,�<�3V. v Ü 36>a<�P�OQ.fl 0t36<aO7x?q/)TCE�,�. �v ��� L 0 h�,4.fl@,�nO7>aO7nkO7q/,�0G;6p��¤.=C7�^�RP�OQ.fl v 0f,�q/./0tO7uv./,�<"./;rÆ�C�)4,��?>a,Ä�@ 0 ��ACB �}���¼t2�9��B �v ��� L 0 ��CU~�l@,�>}wF&óÖ�@ 0 ��AIB ���21� �@G��ACB �}�t÷�Ó3'*P�l@,�>À¿ÿO7q4qfx·�ku�OQ,�>j.f5QA�5�3V0fs6,6C�~)laO�q23V0fsIx?n*,�>c.�O�>a<aO7u�3V./,�q2.fla3V.�PR,&>a,�,�<;I>a5QA�,�q/.f3Vh?5�O7qfl����@CV.I�2p¯;60Ä�@ 0 ��ACB �}��C�~)l@,�0f,�p¯;60f,6w�Pz,&n3^A�<@,�g6,�5Q;6mï.fl@,�ma0f;=;6p�h�,�5Q;^P�hjA 36qfqfxanO�>@s �v ���O7qe365QP�3�AWq�uv;I>j.f36O7>@,�<'P2OQ.flaO7>i3uv;In*m�36uv.�q/,�.8Æ�C

H�,�uv;I>aqfO7<@,�0�;I>a5QA�.fl@,iu�36q/,i;6pe,�g6,�>�qWC(�RA�qfO�n*m?5Q,~-3�AW5Q;60&,v¡=m�36>aqfOQ;I>�;6pxt O7>��¤.=C7�^��PR,"nk3�Aqfl@;^P .fla3V.

�� v þ|� ô Aa�?� ö ��¡ 8 4 L��9ð� H A@�&s �� 8 ã ¡6Ü �o×k� � � 8 t � ã � �9� ôwv ���¯ò=�Is���� ãs���q^� � � 8 t � � � ó65,�f�¯ò=�Cs���� ôwv ÷z�¯ò=�Cs��}� �87 M ¢r£ �¯ò=�6s���� ô

P�l@,�0f,95­� � * � ô �,+�C�)4,��?>@,-� ñ � v þ|� ô Aa�)36q8�� v þ|� ô Aa��P2OQ.fl v O7>'t � � � ó65,�f�¯ò=�Is��}� ôwv ÷�0f,�m�5736uv,�<�h=A �v ��� CE�,�. �v ñ��� <@,�>@;6./,i.fl@,inO7>?O7nO7q/,�0�;6px� ñ � v þ|� ô Aa��wU36>a<�m?x@.��@ ñ ��ACB �}�-� t4�9� ô �v ñ��� ��C�~r;�<@,�0tOQg6,����@CV.I��OQ.qfx·�kuv,�qe./;Zqfl@;^P .fla3V.).fl@,�0t,�qfxa5Q.el@;I57<?q�p|;60��@Iñ6��AIB ����w�36>a<'36<a<aO7.fOQ;I>a36575QA*.fl?3V.

�@G��AIB ���m�J�@ ñ ��ACB �}�I}�� � �¤¥ � � õ �¤�=C7�^�)4,��?>@, : ã �����m� ��¿b¥ ã � � 8 ö  ��¡ 8 ¢0£ �¯ò=�Cs������¯ò=�Cs��}� ã ô

5Q,�.#öTöT���}��<@,�>@;6./,�.fl@,1q�÷#q*n3V./0tOK¡iP�OQ.fl : ��� ã � M ������36q2OQ.fq���¾ ô ×=��£Â.fl ,�57,�n*,�>c.�w�36>a<�m?x@.;�öT��� ô ����� ��� ô � ô�õ�õ�õ�ô �c�EöTö}����� � 8 ��� ô � ô�õ�õ�õ^ô � � � 8 �=< ¢ ���}�36>a<>; ö £ ��� ô ������;�ö����C{¦¥ ô �}��Cz��>�.flaO7qe>a;6.f3V.fOQ;I>'PR,�la3�g6,6w�hjAi.fl@,�<a,��?>aOQ.fOQ;I>";6p1�@IñV��ACB �}��w

�@ ñ ��AIB ����s�@G��AIB ����� ��¿b¥�� � 8 ö ��¡ 8 ; ö £ �¯ò=�Cs�� ô �}� Ý LT�9ð�� H Aa�&s �� 8 ã ¡6Ü �o×·� � � 8 @ � ã � ��AIB ���÷��¯ò � s��}� ã sü��q^� � � 8 t � � � ó65 � �¯ò � s���� ô �vf��� ÷z�¯ò � s��}� � á� ��¿b¥�� � 8 ö ��¡ 8 ; ö £ �¯ò=�Cs�� ô �}� ¡ íw�·}#��q^� � � 8&? @ � � � ó²ACB �=}�5 �� �¯ò � s����t÷sÄt � � � ó65,�f�¯ò=�Cs���� ô �v ��� ÷A@z�¯ò=�Cs��}� � £ ô �¤�=CV.I�

���

Page 21: Methods for Estimating a Conditional Distribution Function ...

P�l@,�0f,�í|�Q� LT�9ð�� H A@��s�@G��ACB ò=���436>a<�5 �� � * � ô �,+�C��N�=,�,6wrp|;60�,v¡@36n*m?5Q,6w«p|;60tn�xa573�� � C7�6�^�4;6p�ùa36>�36>a<�DO �/hT,�5�q������6�6úI��C �(�zA�.fla,�,�0fs6;W<aO7u�.fl@,�;60f,�n�wdöTöT���}�Q� Ò����}�Eö O�>'ma0f;6h�3Vh?O757OQ.yA6waP�l@,�0t,/ö <a,�>@;6./,�q4.fl@,q�÷Äq&nk3V./0tOK¡ZP2OQ.fl[ó·��� ã � M O7>im�;IqfOQ.fOQ;I>���¾ ô ×=��C)4,��?>@,CB��I� Ø 8�D ã D � ó6��8/L ã �Wój�¯ò=�Cs��}�|{¦¥�÷ ã � 8236>a<�8�b� ��q^� � � 8 ? @ � � � ó²AIB ��}-5 �� �¯ò � s��}�t÷:s�t � � � ó65,�f�¯ò=�6s���� ô �v ��� ÷A@ õ��;6.fO7>as�.fl@,)0f,�m?0f,�q/,�>j.f3V.fOQ;I>��¤�=CV.I�Gp|;60-�@ ñ ��AIB ���·s0@G��AIB ����wj36>?<3657q/;�E«,�nn36q2�)36>a<0.D;6p�SU3V;�36>?<k~r;I>@s�����6�! 6��þT36>a<'0f,�u�365757O7>as�.fl?3V. �v ��� � Æ�þaPR,�n�AZma0t;^g6,�.fla3V.�.fl@,�0t3V.fOQ;*;6p"�@ ñ ��AIB ����s�@G��AIB ���e36>a<

��¿b¥�� � 8 Ò����}� � 8 ö ��¡ 8 B�� ¢r£ �¯ò=�Cs����2ófíw��}��8�W�¯ò=�Cs��}� � ÷uv;I>cg6,�0fs6,�q4O7>ima0t;6h?3Vh?O757O7.�A./;��VCÈ�RAZ.fl@,�,�0fs6;=<?O7uD.fl@,�;60f,�n�w

��¿b¥ � � 8 � � 8 Ò������ � 8 ö  ��¡ 8 B�� ¢0£ �¯ò=�Csh���à�8�a�¯ò=�Cs���� � � ù � �����I}�� � ���^� õ�yp�.fl@,BåiO7>ü��B � ��O7q�q/./0�O7uv.f5QAïm�;IqfOQ.fOQg6,*.fl@,�>�OQ.�p¯;I575Q;�P�q�p¯0f;In ~�l@,�;60f,�n �VC� ';6p)+-,�57OQs60t36<������6�6úI��.fl?3V.��¿b¥�� � 8?��M Ø � B�� ¢0£ �¯ò=�Cs��}�^í|��O7qe36q/AWn*ma./;6.fO�u�36575QAi��;60tnk365}P�OQ.fl�n*,�36>��36>a<�gV3V0tO736>auv,

¥ � 8 Mó ¢0£ �¯ò 8 s��}�^í 8 ÷ M }�¥ � 8 ö ��¡ M M óEB 8 ¢r£ �¯ò 8 s����^í 8 B�� ¢r£ �¯ò=�Cs����^íw�y÷ õ~)l@,��a0tqf../,�0tn O�>ý.flaO7q*,v¡Wma0f,�qfqtOQ;I> uv;I>jg6,�0fs6,�qk./;�Ò������à@G��AIB ���?óc�/s�@G��ACB �}�t÷�ø@M� Cj�RAÿE�,�nnk3 �';6pSG;IqflaO7la3V0�3'�����! VúI��w�.fl@,�q/,�uv;I>a<�./,�0tn O7q�h�;Ixa>a<@,�<i3Vh�;^g6,�hjAi3uv;I>aqf.f36>c.�n�xa5Q.fO7m?5Q,4;6p

¥ ��8 � ä �q�­�|8 � ä�� ö ��¡ 8 Ö ��¾�� äQ�­��8 � ä � ôP�laO7u�l}wjO7>g=OQ,�P ;6pU��B � ��w@uv;I>jg6,�0fs6,�q�./;��WCG~)la,�0f,�p|;60t,6wj.fl@,4q/,�uv;I>a<"./,�0tn O7qU36qfA=n*m?./;6.fO7u�36575QA*>@,�sI57O7sIOQh?5Q,6CBR;In�h�O7>aO7>@s�.fl@,�0f,�qtxa5Q.fqeO7>".flaO7q�m�3V0t3Vs60t3Vm?l�PR,�;6ha.f36O7>�waO7>i.fl@,�u�36q/,�å-§ �Ww?.fl@,�g6,�0tqfOQ;I>i;6p)���@CV.I�R.fl?3V.3V0tO7q/,�q�OQp0�@IñV��ACB �}��O7q�0f,�m?5�36uv,�<�h=A�@G��ACB �}��C ~)l?O7q�0f,�qfx?5Q.�uv;I>j.fO7>=x@,�q�./;ïl@;I57<�O7>�.fla,Zu�36q/,[åÄ� �WwG36>a<O7>a<@,�,�<�O7q�0t,�573V.fOQg6,�5QA",�36q/Ai./;ma0f;�g6,�.fl@,�0f,6þ�q/,�,�:),�nk3V0f����O7>'�=,�uv.fOQ;I>'�@C

~)l@,R�?>a365Wq/./,�m*O7q-./;Dma0f;�g6,��¤�=C7�^��CGù@;60tn�xa573*�¤�=CV.I�rma0f;�g=O7<a,�q-36>�,v¡Wm?57O7u�O7.«,v¡Wma0f,�qfqfO7;I>�p¯;60St2�9� ô �v ñ��� �!st2�9� ôwv Ü ��wT36>a<�qfO�nO7573V0t57APz,�n3�A'<a,�0tOQg6,�36> ,v¡=m?0f,�qfqfOQ;I>'p|;60�t � � � �9� ô �v ñ��� ��s�t � � � �9� ôwv Ü ��C)ª20fsIxaO�>@s*.fljx?qPz,�nk3�Aÿma0f;�g6,�.fla3V.�t � � � �9� ô �v ñ��� ��� t � � � �9� ôwv Ü �O7>ýma0f;6h?3Vh�O757OQ.yA6Cü~)l@,�0f,�p¯;60f,6weqfO7>?uv, v Ü O7qxa>?O7�jxa,�5QA<@,�./,�0tnO7>a,�< h=A ���@C7�^��w �v ñ��� � v Ü O�> ma0f;6h�3Vh?O757OQ.yA6C#1�,�>auv,6w/B �v ñ��� s �v���� B½� �WC �WO�>auv,�36575�.fl@, �?0tq/.<@,�0tOQgV3V.fOQg6,�qR;6pÓ�1ñV� v þ|� ô A@�4�¯P�OQ.flZ0f,�q/m�,�uv.�./;*uv;In*m�;I>@,�>j.fqz;6p v �Gg�36>aO�qflZ3V. v � �v ñ��� wW.flaO7q�O7nm?57OQ,�q�.fl?3V.�� �v ñ��� þ|� ô A@���¼�1ñ6� �v ñ��� þ|� ô Aa�I}�� � ��¿b¥aM � ��CR��;�P�w�� �v ��� þ|� ô Aa�m�P�1ñ�� �v ��� þ|� ô A@��C�1�,�>?uv,6w�qfO7>?uv, �v ��� 36>a<�v ñ��� nkO7>aO7nO�q/,:� 36>?<#� ñ w?0f,�q/m�,�uv.fOQg6,�5QA6w

� H �� �v ñ��� þ|� ô A@��s��� �v���� þ|� ô A@���¼� ñ � �v ñ��� þ|� ô Aa��s�� ñ � �v���� þ|� ô Aa�I}�� � ��¿b¥ M � � H � � ��¿b¥ M � � õ���

Page 22: Methods for Estimating a Conditional Distribution Function ...

~)laO7q�,�qf.f3Vh?57O7qfla,�q�.fla3V.2��¿b¥ M � � � 8 ó��� �v ñ��� þ|� ô A@�ksr�� �v ��� þ|� ô A@�t÷��(��O7>*m?0f;6h?3Vh?O75�OQ.�A6C��WO7>auv,)365�[email protected]@,��?0tq/.<@,�0tOQgV3V.fOQg6,�qe;6p��� v þ|� ô Aa���¯P�O7.fli0f,�q/m�,�uv.)./;kuv;In*m�;I>@,�>j.fqe;6p v �zgV36>aO7qfli3V. v � �v ��� [email protected])O7nm?57OQ,�qz.fla3V.¥ � M � � �v ��� s �v ñ��� � <�F�� �v ��� ��� �v ��� ��� �v ��� s �v ñ��� �S� � �¤�=C � �O7>�ma0f;6h�3Vh?O757OQ.yA6w@P�l@,�0f, F�&� v ��,��=xa3657qe.fl@,Eq3÷Äqn3V./0tOQ¡";6pGq/,�uv;I>?<�<@,�0tO7g�3V.fOQg6,�q�w?P�OQ.fl'0f,�q/m�,�uv.)./;Zuv;In*�mT;I>a,�>c.fq4;6p v wT;6pm�� v þ|� ô A@��C�~)la,�5Q,�p¯.���la36>a<�qfO7<@,�;6p2�¤�=C � �4n3^A�h�,�P)0�OQ././,�> 36qHG <I�� �v ��� �,Gkw�P�la,�0f,Go<a,�>@;6./,�qe.fl@,1q���g6,�uv./;604P�l@;Iq/, ¾t£Â.fl',�5Q,�n*,�>j.�O7q�� �v ��� s �v ñ��� �O� � ��{¦¥ � �k��� 8�w?36>a<I�ô� <aO�3Vs?��� ô ¥ � 8 ô�õ�õ�õ�ô ¥ � � � � 8d� � F�� �v���� �=<aO73Vs���� ô ¥ � 8 ô�õ�õ�õ^ô ¥ � � � � 8d� � õ�y.4n3�A�h�,�ma0t;^g6,�< .fla3V. I� � Ò����}�à@G��ACB �}�?óc�:s?@G��ACB �}�t÷}ö�O7>'ma0t;6h?3Vh?O757O7.�A6w@P�l@,�0t,/ö O�q).fl@,�mT;IqtOQ.fOQg6,v�<@,��?>aOQ./,Gnk3V./0tOK¡�<@,��?>@,�<�,�3V0t57OQ,�0-O7>�.fl@,Gm?0f;j;6p�CÁ1�,�>auv,6wV.fl@,m¾f£Â.fl�,�57,�n*,�>c.r;6p �v ��� s �v ñ��� ,��jxa365�qb� � �¤¥ � �k��� 8 �p|;60k� H ¾ H qWC~)l@,<@,�qtOQ0f,�<ï0f,�qfx?5Q.�¤�=C7�^�Dp¯;I575Q;^P2q�p|0t;In .flaO7q�p¯;60tn�xa573i36>a<�.fl@,kp¯36uv.�.fl?3V.À�@G��ACB �}���,v¡=mr� �v ��8d���� �|{cóc�Q}�,v¡Wmr� �v ��8d���� �t÷Iw?P�l@,�0t, �v ��8d���� <a,�>@;6./,�q).fl@,��a0tq/.�,�5Q,�n*,�>j.);6p �vf��� C�Z`zêKJr¨j§"®|¥=©ML?¥��¥NJT\Ibÿ~)l@,il@,�5Qmap9xa5Guv;Inkn*,�>c.fq&;6p2.fl@,i,�<aOQ./;60*36>a<ý3 0f,�g=O7,�Pz,�03V0f,"s60t3V./,�p9xa575QA�36uÊ��=>@;�P�5Q,�<@s6,�<�C

O 4P%²4GéC4Uç&íS4müª2la>�wT1�CG�����6���I��C���;I>am?3V0t36n*,�./0tO�u�.yPz;V��q/.f3Vs6,k,�q/.fO7n3V.fOQ;I> ;6pUuv;I>a<?OQ.fOQ;I>a365-utl@;IO�uv,�ma0t;6h?3Vh?O757O7.fOQ,�q)O7>�3

h?O7>?3V0fAZu�l@;IO7uv,�n*;W<@,�5}xa>?<@,�0)xa>auv,�0f.f36O�>c.yA6CRQà�TS «,©�¸© ¹r��±%´OT « ¯Vw��U��w ��� �� � V�=Cª2la>�wW1�CW36>a<�d�36>aqf�=O�waB4CFùRC������6� � ��C�)DO7q/./0�[email protected];I>k.fl@,�;60fAp¯;60�.fl@,�36>a365QAWqfO7qU;6p«h?O7>?3V0fA*utl@;IO7uv,�xa>?<@,�0

xa>auv,�0t.f36O7>c.yA�P�OQ.fl�>a;I>@m?3V0t36n*,�./0�O7u&,�q/.fO7n3V.fO7;I>�;6p�,v¡=m�,�uv.f3V.fOQ;I>?q�C�Qà�KS «,©�¸© ¹r��±%´OT « ¯VwP�T��w�.6�W���� .W�VC�R3V0thT,6w�+rC�36>a<Ä�R,�0f.f36O75�wa+-Cr�����6���I��CCVW�� � �,T��X�±U� ³�Y½©à© ±¤¯²±%´ ¬ ýzC½�=ma0tO7>as6,�0�wà�R,�0t5�O7>}C�Rl?3V./.f36utla3V0fAI3Ww�+rC ÊCc36>a<���36>@s6;6m?36<aljAI3�A6waª�C Ê*CT�����6�V�c��CÈÊ�,�0t>@,�5?36>a<>@,�3V0f,�qf.���>@,�OQsIljhT;60z,�q/.fO7n3V.fO7;I>;6p�3uv;I>a<aO7.fOQ;I>a365��jx?36>c.fO757,6CPZ ¸k¸ �\[6± ¬ ±¤T�¯²±|�Kw���]}w«� �I�6���t� �a�²�=C

B�ljx�w�BDC �UÊ*C}36>a<�B�l@,�>@s@wCÊ*CFùRCG�����6���I��C��2;I>@m?3V0�36n*,�./0tO7u�0f,�s60f,�qfqtOQ;I>�,�q/.fO7n3V./,�q�x?qfO7>@s"nO7qfu�5736qtqfOQ�a,�<h?O7>?3V0fAk0f,�qfmT;I>?q/,�q�C Y T © ¹r��±%´OT_^ ¬ w�]2��w � �²�^� � .��=C

B�ljx�waBDC �UÊ*C=36>?<id 3V0f0f;I>�w@�aC��TC}�����6�W�^��C�B�l@;=;IqfO7>as�3��6,�0t>@,�5T0f,�s60f,�qtqfOQ;I>",�q/.fO7n3V./;60^C`[6± ¬ ±¤T�¯²±|�\[ « T�� ¸6« ��}w��I�¦���®� � ú=CBR;6m?36q�w��@C �4CÁ�����6���I��C2E�;Wu�365r57O7�6,�57O7l@;=;=<"h?36qf,�<';I> �6,�0t>@,�5«uv,�>?q/;60tO7>@s@CaQà��b ©*ò �&[6± ¬ ±¤T�¯²±|�&[ ©·« �/[k�­´�� Y���Tw.�.W���à. � �=Cùa36>}w=�aCa�����6� � ��CUE�;Wu�365@57O7>@,�3V0Á0f,�s60t,�qfqfOQ;I>&qfn*;=;6.fl@,�0tq�36>?<&.fl@,�OQ0�nO7>aO�n3�¡�,��ku�OQ,�>?u�OQ,�q�CWZ ¸k¸ �W[6± ¬ ±¤T°¯²±|��ð�?w«���6ú^�à.W��ú=C

.V�

Page 23: Methods for Estimating a Conditional Distribution Function ...

ùa36>}w-�aC�36>a<��DO �/h�,�57q�wT��CU�����6�6úI��Cdc ©·«­¬¦¨feS©�¨�ò·¸© ¹0T ¬¦¨fgÀ©·³ � ¨�¨ T ¸ � ¬¦¸C³ TN±¤¯hZ5ý{ý ¨ T «­¬ ±¤T ©�¸ ¯²��B�la3Vm�n36>36>a<'1436575�waE«;I>a<@;I>}C

ùa36>}w4�awGSU3V;@w�N�Cz36>a< ~r;I>@s@w�1�CD�����6�6úI��Cz$Uqf.fO7n3V.fOQ;I>�;6p�uv;I>a<aOQ.fO7;I>a365�<@,�>?qfOQ.fOQ,�qZ36>a<üq/,�>?qfOQ.fOQgWOQ.�An*,�36qfxa0f,�q)O7>'>a;I>a57O7>@,�3V0e<@AW>a36nO�u�365}q/A=qf./,�nq�C Y T © ¹r��±%´OT_^ ¬ w�]$û}w«���6���d.V�Iú=C

1236575�wa+rC�36>a<'+G0t,�qf>@,�575�w^�4Cr�����6�! 6��C���>j./,�>j.fOQ;I>a36575QAj��h?O736qf,�<Zh�;=;6.fq/./0t3Vm�n,�.fl@;=<?q�CUd�36>=xaqfuv0�OQma.�C1236575�w-+-Cr36>?<�~-x@0t5736u�l}w&�4CÂH�C������6�! 6��C���>j./,�0fm�;I573V.fOQ;I>�n*,�.fl@;W<aq�p¯;60�36<a3Vm?.fO7>@s'./;ïq/m?3V0tqf,k<@,�qfOQsI>�O7>

>@;I>@m�3V0t36n*,�./0tO7uD0t,�s60f,�qfqfOQ;I>��¯P�OQ.fl�<aO7qtu�xaqfqfOQ;I>T��C\Q^�TZ:¹��­´��\[6± ¬ ±¤T�¯²±|�\Z:¯w¯ ©^« �Kw�i2��wk�cú6ú^�®�î Vú=C1��/;60f.�w���CFEUCr36>a<��6;I>@,�q�w�d�C B4C������6�6úI��C�E�;Wu�36575QAïm?3V0t36n,�./0tO7u>@;I>am?3V0t36n*,�./0tO�u<@,�>aqfO7.�Aï,�q/.fO7n3V.fO7;I>}CZ ¸k¸ �\[6± ¬ ±¤T�¯�±|�Kw2�Eþ«w«��úW���^����ú��î jC�6;I>@,�q�w?d�C B4Ca36>a<i1436575�w@+-C«�����6�V�c��C�d�,�36>'qf�=xa3V0f,�<",�0f0t;60ema0f;6m�,�0f.fOQ,�qR;6p«�6,�0�>@,�5�,�q/.fO7n3V./,�q);6p«0f,�s60f,�q/�

qfOQ;I>�C`[6± ¬ ±¤T�¯²±|� e ´ © µ ¬ µ·�fc���±|±|�D��j�wÖ.6� � �d.6�6�=CÊ�5Q,�O7>}w@:�CÂH{Cr�����6� � ��Cx�=m�,�u�OQ��u�3V.fOQ;I>i./,�q/.fq)p¯;60)h?O�>a3V0fAZu�l@;IO7uv,�n;=<@,�5�q�h?36q/,�<�;I>'O�>a<@,v¡"�=xa36>j.fO75Q,�q�CkQ^�S «,©�¸Ö© ¹r��±%´OT « ¯Vw���i}w � � � � � ¦�=CE�;I36<@,�0�w�B4CF:�Cr�����6�6úI��C�E�;Wu�365�57O7�6,�57O7l@;=;=<"<@,�>aqtOQ.�A",�q/.fO7n3V.fO7;I>}CPZ ¸�¸ �\[6± ¬ ±¤T�¯²±|�Kw��Eþ�wr��úV�!.^����úW���=Cd�3V.|É��WO7>}w=:�CFEGCT�����6��.I��CU��;I>am?3V0t36n*,�./0tO�ue36>a<<aO7qf./[email protected];I>W��p|0t,�,U,�q/.fO7nk3V.fOQ;I>&;6p�.fl@,eh?O7>a3V0tA�.fl@0f,�qtl@;I57<

uv0f;IqfqtO7>@s36>a<�.fla,�h?O7>a3V0fA"utl@;IO�uv,�n*;W<@,�57q�CPS «,©�¸© ¹r��±%´OT «­¬ w���j}wÖ. � �^�à.! ��WC+r,�5�OQs60t36<}wGd�CR�����6�6úI��C�:),�uv,�>j.�36<ag�36>auv,�q&O7>�.fl@,Zuv,�>j./0t365R57O7nO7.�.fl@,�;60f,�n 36>a<�O7.fq�PR,�3V��O7>jg�3V0�O736>auv,

ma0tO�>au�OQm?5Q,�p|;60�nOK¡@O7>@s"q/,��=x@,�>auv,�q�;6pz0t36>a<@;In gV3V0tO73Vh?5Q,�q�C4��>Cþmí �QýS� ¸6³ � ¸6« �ET ¸le ´ © µ ¬ µ!T ¨ TN± òÀ¬¦¸6³[6± ¬ ±¤T�¯�±¤T « ¯Vwk$U<}C�$�C�$Gh�,�0t57,�O7>Z36>?<�d�C���C?~r36�=�=x}C���OQ0f�Wlnm36xaq/,�0�wk�R;Iq/./;I>�w«��� � �d.�. � C+G0f,�qfq�wcH�CF1�CQw@~r,�x@�6;I57q/�=A6w^�TCFª�CQw�o�,�././,�0t57O7>@s@wjH{CF~�Cj36>a<ùÁ5736>?>@,�0fA6wî�4CF+-CT�����6��.I��C��-¶!¹r�­´OT «­¬¦¨ b�� « T ýS�,¯T ¸ ñ�C�B�36n�ha0tO7<as6,1è2>aO7g6,�0tqfOQ.yAZ+G0t,�qfq�wTB�36n�ha0tO�<@s6,6C:�x@mam�,�0f.�w&)�Cr36>a<�H�36>?<}wGd�CF+-CR�����6���j��C�d�xa57.fOQg�3V0�O73V./,*Pz,�O7sIlc./,�<�5Q,�36q/.�qf�jx?3V0f,�q�0f,�s60t,�qfqfOQ;I>}C�Z ¸k¸ �[6± ¬ ±¤T�¯�±|�Kw2�{�}w«� � �cú^��� � ��WC�=,�OQp¯,�0f.�w�4C�36>?<À�D36qfqf,�0�wT~�Cr�����6�6úV3c��C2ùÁO7>aO7./,v��qf36n*m?5Q,�36>?365QA=qtO7q);6p�5Q;Wu�365�m�;I5QAW>@;InO7365�q�þG36>a365QAWqfO7q236>a<

q/;I57xa.fOQ;I>aq�C�Qà��Z:¹r�­´f�\[6± ¬ ±¤T�¯²±|�PZ8¯w¯ ©·« �Kw�i��aw.6ú! ��à.! ¦�=C�=,�OQp¯,�0f.�w®�4Cc36>a<0�D36qtq/,�0�wj~�C?�����6�6ú�hT��CPoG3V0tO736>?uv,)ma0f;6m�,�0f.fOQ,�q-;6p}5Q;Wu�365Wm�;I5QA=>a;InO73657q-36>a<*,�>aqtxaO7>@sDn*;W<W�OQ�?u�3V.fO7;I>aq2�¯P�O7.fl<aO7qfu�x?qfqfOQ;I>���wjO7>d[6± ¬ ±¤T�¯�±¤T «­¬¦¨ VW�Ö� © ´ òr¬¦¸6³ ñ © ¹�ý�¶·± ¬ ±¤T ©�¸�¬¦¨ Z:¯eýS� « ±¤¯ ©zî [^¹ ©à© ± ��pT ¸ �Áw@,�<aq�C�H�C?1qm3V0t<a5Q,�36>?<�d�C��&CÖ�Wutl?O7n*,��TCG+UljA=qfO�u�3��ro�,�0t573Vs@w�12,�O7<@,�57hT,�0ts@w=m?m�C��V���^ V�=C�Wl@,�3V.fl@,�0�wk�TCÆ�aCj36>a<"d�3V0f0t;I>}wW�aC��TCT�����6�V�c��CÈÊ�,�0t>@,�5��jx?36>c.fO757,),�q/.fO7n3V./;60�q�CkQà��Z:¹r�­´f�\[6± ¬ ±¤T�¯²±|�WZ8¯w¯ ©·« �Kw]��}wk�a�����N�a��ú=C�WO7n*;I>@;VJÁw?�@C���C«�����6�6úI��CR[^¹ ©î© ± �kT ¸ � g ��± � ©·³ ¯:T ¸ [6± ¬ ±¤T�¯²±¤T « ¯²�m�=ma0tO�>@s6,�0�wW��,�P SG;60f��C

SU3V;@wzN�Cz�����6���I��CïB�;I>a<aOQ.fOQ;I>?365Áma0f,�<aO7uv.fO7g6,*0f,�sIOQ;I>aq�p|;60�q/./;=u�la36q/.fO7uZma0f;Wuv,�qfq/,�q�C�è4>aOQg6,�0tqtOQ.�Aï;6p<Ê�,�>j.~r,�utla>aO�u�365�:),�m�;60f.<è8ÊDB&����dh�T�V�6ús�=�� jC

SU3V;@wjN�C�36>a<�~r;I>@s@wV1�Cc�����6�! 6��CG�2;I>@m?3V0t36n,�./0tO7u�,�q/.fO�n3V.fOQ;I>�;6p=0t3V.fOQ;Iq};6p@>@;IO�q/,�./;�qfOQsI>?3656O7>�q/./;Wutla36q/.fO�u0f,�s60f,�qtqfOQ;I>aq�CUd 36>=xaqfuv0tOQm?.�C

SG;IqflaO7la3V0�3Ww<Ê*C4�����! VúI��C�E«O7nO7.fO7>@sïh�,�la3�gWOQ;Ix@0Z;6p�è���q/.f3V.fO7qf.fO7u�q"p|;60"q/.f3V.fOQ;I>a3V0fA 3Vh�q/;I57x@./,�5QAý0f,�sIx?573V0ma0f;Wuv,�qfq/,�q�C�t�� �0¬ �·´O¯ « ��,T ¸�¨ T « �T^î�,TN±¤¯²± �� © ´OT��Hu��­´ �av<�¦µ·�Kw2û���wÖ. � ^�d.���.=C

.W�

Page 24: Methods for Estimating a Conditional Distribution Function ...

SUx}w�Ê*Ca36>a< �6;I>@,�q�wTd�C B4C«�����6�6�I��CeE«;=u�365�5�O7>@,�3V0)�=xa36>c.fO�5Q,D0f,�s60f,�qfqfO7;I>}CkQà�,Z8¹r�­´��`[C± ¬ ±¤T�¯²±|�PZ8¯w¯ ©·« �

.�.


Recommended