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& Statistics University of Montreal CP 6128, Suc. A Montreal, Quebec H3C 3J7 CANADA

Contributed Papers

ANTONIADIS, A AND GREGORIE,· G.: Nonparametric estimation in change-point hazard rate models for censored data.

ARNOlD, B.C.: Nonparametric estimation of Lorenz curves. BIRGE, L AND MASSART,· P.: Lower bounds for rates of convergence of M.L and

related estimators. BROOKS, M.M.: Bandwidth selection for intensity estimates. DINGIWGLU,· H. AND SUNGUR, E.: The use of copulas in extreme theory. ENGEL, J.: Semiparametric model estimation in nonlinear regression. FALl<, M. AND REISS,· R-D.: Estimating conditional curves: Nearest neighbor

approach. GOZAW, P.L.: A consistent model specification test for kernel estimation of regression

on functions models. KAGAN, A: Quasi likelihood and the projection method for solving the maximum

likelihood equation. KAZAKOS, D.: Asymptotically tight error bounds for multi-hypothesis testing through large

deviation theory. KITSOS, C.P.: Nonparametric features on optimal experimental design. KOKOLAKIS, G.B.: Nonparametric Bayesian prediction in multivariate binary discriminant

analysis. POLITIS, D.: Bootstrapping time series via autoregressive approximations. RICE, J.: Bayesian restoration of single-channel patch champ recordings. STADTMOLLER, U.: Estimation in a multiplicative regression model. UZUNOGULLARI,· U. AND WANG, ** J.-L: Estimation of the hazard function and its

derivatives under random truncation models. WAND, M.P.: Exact mean integrated squared error for dependent data. Y AKOWITZ, S.: Nonparametric regression for Markov sequences without mixing

assumptions.

* Presenter of paper * * Also, a participant

699

INDEX

Abelian groups Abramson absolute error

680 141

566,569 accuracy of the bootstrap confidence

intervals 114 actual average squared errors for

estimation adaptive additive models Ahmad almost i.i.d. errors almost stationary processes almost sure convergence AMISE a-mixing approximation error AR(l) process AR(2) model asymptotic covariance asymptotic distribution asymptotic efficiency asymptotic error exponent asymptotic linearity asymptotic normality asymptotically efficient asymptotically normal autocorrelation autocorrelation operator autocovariance function automatic estimate automatic kernel estimates automatic selection autoregressive function(s) autoregressive model autoregressive processes average curve average derivative estimates average derivative estimator average squared error Azuma inequality

203 145,146,159

499 477 115 389 509 254

273,275,444,446 561,567

378 383 321

321,648 167 634 288

152,443,444,450,456 321 443 378 409 553

16 15

201,548 271,278

607 272 99

167 169 274 352

bandwidth(s) bandwidth choice bandwidth factorization

20,67,148,251,589,590 141 255

bandwidth selection Bayes estimates

241,274 339

Bayes optimal probability of error Bayes risk consistencies

567 347

701

Bell 477 Bell-Pitman function 487 Beran 318 Bernstein('s) inequality 570,572,575 Bernstein-type inequality( -ies) 272,573 Bhattacharya and Mack 144 bias 379 biased cross-validation 256 Bickel 226 Bickel and Wichura 145 Bieren's estimate 16 Billingsley 145,225 bispectra 406 Blaschke's selection theorem 228 b1ock-circulant 202 blur matrices 205 Boneva, Kendall and Stepanov 226 Bonferroni method 121 Boos 226,236 bootstrap 111,114,440,501,577,585,586 bootstrap confidence intervals 122 boundary effects 114 bounded influence function 297 bounded influence regression 297 bounded lipschitz distance 232 bounds of the statistical risk 561 Bowman 238 Bradley 421 Bretagnolle-Hubert kernel 3 Brownian bridge process 410 Brownian bridges 215 Buckley and James 316 bumphunting 126 bump-hunting problem 226 bumps 226

cascade and parallel connections Cauchy density censored data censoring variable chaotic systems Chebyshev's inequality Chernoff Chernofrs bound Chernofrs bounding method Choi circle classes of images

541 236,618

315 432 531

37 147,570,574

31,34 33

477 680

669,670

702

class-fit detectors 478 classification 671,673 classification error 671 classified image 673 clean U-statistic 117 codelength 563,569 compact 682 complexity(-ies) 561,563,566,567,568,570,571 complexity penalty(-ies) 561,562,568 complexity regularization 561-63,565-70,572-73 complexity regularization estimator 573 complexity regularized 569 composite alternative 631 conditonal density estimates 463 conditional distribution 616,617 conditional heteroskedasticity 297 conditional mean 614 conditional median estimator 616 conditional median function 613,614,616 conditional quanti1es 617,621,625 conditional variance 618 conditionally independent 321 confidence band 215 confidence bands for the quantile

function 215 confidence intervals 114,619 conservative confidence bands 45 consistency 129,130,555 consistent test 631 continuity of a Brownian Bridge process 221 continuous time process 509 continuous time stochastic process 553 control variables 531 convergence rates 249 converges at rate 570 converges to zero at rate 569 convex minorant 193,195 convolution 682,683 corrected v-fold cross-validation 606 correlated residuals 75 covariance operator 509 covariate 587,588,595,597 coverage probability(-ies) 577,578,579,583 Crist6bal, Faraldo and GOIlZlilez-Manteiga 320 cross-validated 23,262 cross-validationl1 ,67,241,261,274-77 ,279 ,366,603 cross-validation functional 322 Csorg5-Revesz-Stute ([CRS]) conditions 19 Cuevas 236 cumulative hazard rate function 316

curve estimation 141

Dabrowska 318 DasGupta and Studden 339 data-based 249 data compression 561 data-driven bandwidth 20 data-driven estimator 26 deconvoluted kernel 615,616,623,624 deconvoluted kernel density estimators 614,615 deconvoluted kernel estimates 623,624 deconvoluted kernel estimator(s) 617,618,621 deconvoluted kernel function(s) 622,625 deconvoluted kernel median function

estimators 616 deconvoluted kernel method 614 deconvoluted kernel regression function

estimator(s) 616,619 deconvolution 203,614,618,625 degraded images 201 degrees of censorship 321 Deheuvels' estimate 16,40 DeMontricher 125,131 Demm1er and Reinsch 344 Demmler-Reinsch basis 344 density 173 density estimates 19 density estimation 125,280,561 density estimation-free confidence bands 217 density estimation on Stiefel manifolds 683 density function 218 dependent competing risks 431 derivative(s) 69,145,160 design-adaptive 619,620,625 design-adaptive method 614 design-adaptive quantile estimators 626 design choice 675 deviation 148 Devroye 227 Devroye and Gyorfi 419 Dharmadhikari and Joag-dev 235 diagnostic capabilities 129 diagonal expansion 543 diagonal series expansion 543 differential entropy 81 diffusion process 553 dimensionality problem 280 discrete observations 553 distance between 119 distance measure 632

distortion function( s) distribution-free bounds distribution function distribution of functionals divided differences Doeblin's hypothesis Doob martingale

566,567,568,569,570 358 215 112 339

double exponential dynamic systems

Eddy edge estimation edge estimator efficient Efron-Stein inequality eigenvectors elliptically contoured empirical distribution function empirical measure empirical probability measure empirical processes empirical quantile function energy transfer entropy estimators equispaced grid error distribution errors-in-variables errors in variables model on

the sphere estimated mean squared error estimating derivatives estimation cross-validation estimation of the derivatives exponential bounds exponential inequalities extraneous statistical noise

FFfs finite order kernels fixed design fixed design model t/>-mixing condition Fourier integrals Fourier matrix Fourier representation frame-grabbing functional

443,444 32,41

618 531

148 669,672,675 673,675,677

145,146,159,164 40

509 173

19,35,261-62,264 91,633

38 19

213 406

81 670,671,675,676

618 614,625,679,680

680,681,689 367 241 201 277 347

31 488

202 4

315 112

273,445 407 202 406 205 243

functional laws of the iterated logarithm 19

Gaussian mixture Gaussian process( -es) GCV

703

477

generalization of the MPLE generalized additive models (GAM) generalized kth divided difference generalized Lehmann alternative

142,148,272 203 128 280 345

model(s) generalized maximum likelihood

estimates geometric ergodicity geometrically ergodic global rates of convergence Good and Gaskins goodness-of-fit goodness-of-fit detectors Gorodettski Gram-Charlier kernels Grenander Gyorfi Gyorfi, HardIe, Sarda and Vieu

Hall halving approach Hausdorff metric Hart and Vieu Hasminskii hazard rate estimation

448,647

434 444 443 358

125,131,226 122 478 420

10 147 419 419

231,234,238 121 228 419

672,677 280

h-block cross-validation Heckman and Woodroofe Hellinger distance heteroskedastic regression heteroskedasticity Hettmansperger

603,604,608,609,610 341

Hettmansperger and Klimko high dimensional linear models higher order kernel( s) Hilbert space Hilbertian autoregressive process histogram histogram estimate Hoeffding Hoeffding's inequality homoskedastic Huber Huber's .J--function hypothesis testing

lbragimov

567,570,573,574 287 297 226 226 123

241,255 679,687

509 632

36,42 31,570

31,33,571,572 321 232 298 631

Gamma 618 identification problem 420,672,677

494

704

I-divergence 89 ill-posed problems 202,679 image analysis 669,676 image and edge estimation 669,674 image and edge estimators 674 image estimation 669,670,672 image estimator 673,675 image restoration 201 ~SL 129 ~SL-subroutines 238 increments 19 index of resolvability 561,563-65,567-69,571-74 indices of approximation 568 inflation rate 362 inflection points 226 influence function 126,127,129 integrable nonparametric models 657 integral equation 543 integrated mean squared errors (IMSE) 144 integrated squared error (ISE) 274 interaction 377 inverse estimation 191 inverse problem 191,195 inverse triangular density 622 inversion 195 IF-method 227 isotropic 4(J7

Izenman and Tran 420

Johnson family of curves 379

Kaplan-Meier 316 Karlin 342 k-dimensionallinear parametric model 120 kernel(s) 147,320,389,591 kernel classification rule 347 kernel density estimate(s) 94,463 kernel density estimation 141,241,419 kernel estimate(s) 20,42,126-27,331,443,588-89 kernel estimator(s) 67,112,146,261-62,264,616 kernel function 146,378 kernel nonparametric techniques 531 kernel of order k 146 kernel of order (m,p) 7 kernel-quantile-density estimator 216 kernel regression 361 kernel spectral estimates 122 kernel-type estimator 173 Klonias 126,130,131,251 k nearest neighbour 320

kn-NN estimate Kolmogorov Kolmogorov entropy Kolmogorov-Smimov distance Kolmogorov-Smimov statistics Korostelev Koul, Susarla and Van Ryzin Krieger and Pickands k-th nearest neighbor Kullback-Leibler loss

Laguerre kernels laws of the iterated logarithm Lay Leamer least squares cross-validation least squares estimate least squares method Lebesgue measure of symmetric

difference Legendre kernels Legostaeva and Shiryayev life time distributions LIL linear estimate linear estimators linear regression model linear smoothing linewise procedure linewise processing Lipschitz condition local bandwidth local bandwidth choice local means local medians local polynomials locally mixing (LM) log-likelihood based distortions log-odds ratio logistic distortion logistic distortion function logistic regression logistic transformation LOOve Ll-consistent density estimator Ll-discrepancy Ll-distance Ll-error Ll norm Ll strong consistency

331 480 138

42,647 35,481

677 317,318

141 22,39

234

10 19

228 339 256 136 316

673 lO

339 431

21 676 676 315 676 676 676 253 141 367 46 46

625 419 569 567 566 566 566 621

130,131 81

620 89,632

673,674 35,252

463

Lp-error L2-approximation error U-approximation to the empirical

674 563

distribution function L2-discrepancy L2-distance Lui

Mack and Miiller Mallow's CL Mann-Whitney Statistic Marcinkiewicz Markov chain(s) Markov process(-es) Marron martingale martingale difference martingale difference sequences martingale-like Masry Massart's bound maximal invariants maximal statistical noise maximum penalized likelihood McDiarmid mean absolute difference mean integrated Ll and L2 errors mean integrated square error

6 619 117 477

143 204

647,649,652,653 130 606

272,443,444,445 231

32 635 32

604,606 419 35

487 478 125

32,34 206 218

(MISE) 21,241,252,274 mean squared error (MSE) 144 mean squared errors for estimation 203 measurement errors 614,616,617,620 measures of deviation 413 median(s) 671 M-estimators 297 Miller 316 minimal sufficient statistic 478 minimax Bayes estimate 339 minimax lower bounds 674 minimum complexity density estimation 561,575 minimum complexity estimator 574 minimum description-length criteria 561 minimum description-length paradigm 561 minimum description-length principle 562,567 minimum variance 655 mixing condition(s) 272,509 mixing processes 389 mixture 649 mode estimation 146 mode estimator(s) 159,160

model selection mollifier Monte Carlo MPLE MR -estimates multidimensional mean squared error multipararneter Gaussian process multiple kernel estimation procedure

for the density multiple minima multivariate density estimates multivariate kernel estimate multivariate nonparametric regression Miiller Miiller and Prewitt Miiller and Stadtmiiller Miiller and Wang

Nadaraya Nadaraya-Watson Nadaraya-Watson estimate Nadaraya-Watson estimator Nadaraya-Watson weighting Nash Navier-Stokes equation

705

561,562,565 3

405 126,127,128

287 322 164

11 209

12 247 163

144,161 163,164 142,162 161,162

143,322 69

378 143 322 130 405

nearest neighbor density estimator nearest neighbors

20 300

16 672,677

576 561,564 ,565 ,575 ,576

nearest neighbour estimate Nemirovskii neural net( s) neural network(s) noise estimate nonlinear autoregressive time series nonlinear functions nonlinear model nonlinear time series nonparametric nonparametric deconvolution feasible nonparametric density nonparametric density estimate nonparametric density estimation nonparametric estimate nonparametric estimation nonparal11etric FPE criterion nonparametric maximum likelihood nonparametric pilot estimator nonparametric prediction nonparametric regression

209 122

564,565 531

493,541 553 626 133 82 35

443,444 31,431

495 192,193

226 389

111,133,329,357,377 ,542,587-88, 590,595,597,672,676

706

nonparametric regression analysis normal not identically distributed errors numerical optimization Nussbaum

observational studies

613 618 119 130

340,672,677

587 optimal choice of It" for mean integrated

L1 and L2 errors 220 686 162

optimal convergence rates optimal local bandwidth optimal rates of convergence optimisation ordered data ordinary cross-validation ordinary kernel functions ordinary kernel regression function ordinary smooth

669,674 202 553

603-06,608,610 623,624

619 617,618

226 543

11

Orear and Cassel orthogonal functions orthogonal polynomials orthogonal polynomials with weights orthogonal series

10 389 544 114 207

orthogonal series estimate oversmooth bandwidth oversmoothed

pair-matching pairwise resampling Papantoni-Kazakos and Kazakos parametric regression model Pareto renewal process Park partition partitioning estimate Parzen Parzen-Rosenblatt kernel estimate peaks penalized likelihood penalty functional Pham and Tran Phillips Curve

587,588,595,597 116 419 119 478 477 632 333

142,147,420 3

141 340 125

piecewise concave/convex functions

419,420 363 134

226,229 134

162,254 26

256 67

277

piecewise convex-concave piecewise monotone functions pilot estimator( s) plug-in estimator plug-in method plug-in rule plug-in techniques

pointwise confidence intervals Polasek polynomial regression polynomials Pratt prediction prediction band(s) prediction ellipsoid prediction error prediction interval(s) prediction region(s) predictor Priestley and Chao probablity centered probability centering probability density function probability of error project pursuit regression (PPR) projection pseudo-likelihood ratio test

quadratic splines quantile(s) quantile density function quantile function(s) quantile matching quantile process

121 339 561

563,564,565,614 677 203

577,579,581,582 581 604

577,578 578,581,586

509 142

581,582 577

81 567 280 499 379

607 443,444,446

218

quantitative measures of smoothness

213,620 652 214 133

random delta sequence random design random right censorship randomized procedures rate(s) of convergence

14 673 315 489

251,569,572,577,579,585,617 rate of improvement 657 recursive kernel density estimates 39 regression 67,339 regression estimation 329 regression function 142,316,613,617,625 regression model 298 regression spline 133 regular and irregular nonparametric

problems regularization regularized deconvolution regularized deconvolution on the circle regularized inverse relative entropy relative entropy distance

657 201,562

680 685 681 574

567,574

relative stability repeated measurements reproducing kernel

37,39 377

5 reproducing kernel Hilbert-subspace residual resampling

5 113

571,573 340

444,445,446,455 419 297

144,147,157,158

resolvability restricted minimax estimates p-mixing Robinson robust regression Romano root-density Rosenblatt Roussas running mean

126 142,420

273,419,420 671

Sacks and Ylvisaker 339,340 Sager 147 sample distribution function 657 sample of curves 99 Scheffe's theorem 225 score function 218 Scott, Tapia and Thompson 126,131 seasonal fluctuations 389 second order admissibiilty 657 second order optimality theory 657 second order spectra 413 selection bias 563 selection of lags 497 semiparametric 553 semiparametric estimation 647 semiparametric weighted least squares 299 semiparametric weighted M-estimator 300 Sethuraman 226 shape parameters 112,133 shift functions 99 shift operator 103 signal detection 477 Silverman 126,131,158,161,225-27,233-34,236 simple hypothesis 631 simulations 257 simultaneous coverage probability 121 simultaneous error bars 121 Slepian lemma 47 smoothed bootstrap 118 smoothed bootstrap estimate 255 smoothed cross-validation 255 smoothed quantile process 220 smoother 671 smoothing 671,676

smoothing factor smoothing matrix smoothing

707

35 202

parameter(s) 20,144,201,261,267,378,548 smoothing parameter selection 241,268 smoothing techniques 272 smoothness assumptions 133 smoothness classes 136 smoothness conditions 92 Sobolev space(s) 125,564,687 Speckman 340 spline(s) 563,564,604,605,607 squared deviance between the parametric

fit and the non parametric fit squared error

121 566,569 566,567

569 480 610

squared error distortion squared error distortion function stable processes stationary Gaussian process stationary process Steele's inequality Stiefel manifold Stone Strassen strictly positive Hermitian strong consistency strong mixing condition

607 41

680,683 231,234,670,672,677

19 681,687 329,443

419 strong uniform consistency of random

kernel-type density estimates structural average structural functional structural points Stute and GonzaIez-Manteiga sup-norm super smooth supremum distance survival function Sweeting symmetric stable laws system modeling

tail condition tailor-designed methods Tapia and Thompson test statistic testing statistical hypotheses tightness time series analysis total variation Tran

12 104 102 99

320 19

617,618,625 236 431

226,229,236 486 533

93 227

125,131 632 477

145,153,156 541 631 420

708

transformations transformed kernel estimate transition distribution function treatment-covariate interaction treatment main effect trend curves trigonometric series Tsybakov turbogenerator set two-dimensional problem two-sample detectors

unbiasedness undersmoothed unemployment rate

605 16

443,444 587-89,595-96

588,589 3n

563,564 669,672,676,6n

533 74

478

554 207 362

uniform deconvolution problem uniform empirical quantile function uniform mixing samples

191,192 213 463 214 478 329

uniform quantile process uniform renewal processes universal consistency U-statistic 117,591

Vapnik-Chervonenkis bound 38 Vapnik-Chervonenkis dimension 38 variable kernel density estimates 242 variable kernel estimates 39 variance 410 v-fold cross-validation 603,604,605,609

Wahba 344 Watson Watson-Nadaraya approach Watson-Nadaraya estimate Watson-Nadaraya kernel estimate Watson-Nadaraya method

143,322 2n 273 273 272 406 wave number vector

weak consistency weak convergence weakly stationary process Weerahandi and Zidek Wegman

329 144,148,153,156,164

553 339 419

weighted averaging of rounded points (WRPing)

weighted linear regression weighted M-estimates weighted R-estimators Wiener process wild bootstrap wild bootstrapping

113 620 289 287

149,411,488,554 111,119

119

Wolf sunspot numbers wreath product group

Yakowitz Yoshihara

zero-one distortion zero-one distortion function

502 487

419 419

569 566