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

[11]

KOROSTELEV AP, 1993, TEOR VEROYA PRIMEN, V38, P857

[12]

Lepski O. V., 1992, ADV SOVIET MATH, V12, P87

[13] Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point [J].

Lepski, OV ;

Tsybakov, AB .

PROBABILITY THEORY AND RELATED FIELDS, 2000, 117 (01) :17-48

[14]

Lifshits M. A., 1995, Gaussian random functions, V322

[15]

Neumann MH, 1997, ANN STAT, V25, P38

[16]

NUSSBAUM M, 1986, THEORY PROBABILITY I, V31, P118

[17]

PITERBARG V, 1996, TRANSL MATH MONOGR, V148

[18] OPTIMAL GLOBAL RATES OF CONVERGENCE FOR NONPARAMETRIC REGRESSION [J].

STONE, CJ .

ANNALS OF STATISTICS, 1982, 10 (04) :1040-1053

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