Asymptotically exact minimax estimation in sup-norm for anisotropic Holder classes

被引：11

作者：

Bertin, K ^{[1
]}

机构：

[1] Univ Paris 06, Lab Probabil & Modeles Aleatoires, F-75252 Paris 05, France

来源：

BERNOULLI | 2004年 / 10卷 / 05期

关键词：

anisotropic Holder class; minimax exact constant; uniform norm; white noise model;

D O I：

10.3150/bj/1099579160

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the Gaussian white noise model and study the estimation of a function f in the uniform norm assuming that f belongs to a Holder anisotropic class. We give the minimax rate of convergence over this class and determine the minimax exact constant and an asymptotically exact estimator.

引用

页码：873 / 888

页数：16

共 18 条

[1]

Adler RJ, 1990, INTRO CONTINUITY EXT

[2] Risk bounds for model selection via penalization [J].

Barron, A ;

Birgé, L ;

Massart, P .

PROBABILITY THEORY AND RELATED FIELDS, 1999, 113 (03) :301-413

[3]

BERTIN K, 2004, IN PRESS J STAT PLAN

[4] ASYMPTOTIC MINIMAX RISK FOR SUP-NORM LOSS - SOLUTION VIA OPTIMAL RECOVERY [J].

DONOHO, DL .

PROBABILITY THEORY AND RELATED FIELDS, 1994, 99 (02) :145-170

[5]

GIHMAN I, 1974, THEORY STOCHASTIC PR, V1

[6]

Gradshteyn IS, 1965, TABLE INTEGRALS SERI

[7]

Ibragimov IA, 1981, STAT ESTIMATION ASYM

[8] Nonlinear estimation in anisotropic multi-index denoising [J].

Kerkyacharian, G ;

Lepski, O ;

Picard, D .

PROBABILITY THEORY AND RELATED FIELDS, 2001, 121 (02) :137-170

[9]

Klemelä J, 2001, ANN STAT, V29, P1567

[10] The asymptotic minimax constant for sup-norm loss in nonparametric density estimation [J].

Korostelev, A ;

Nussbaum, M .

BERNOULLI, 1999, 5 (06) :1099-1118

← 1 2 →