On minimax wavelet estimators

被引：94

作者：

Delyon, B ^{[1
]}

Juditsky, A ^{[1
]}

机构：

[1] INST NATL RECH INFORMAT & AUTOMAT,INISA,F-35042 RENNES,FRANCE

来源：

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 1996年 / 3卷 / 03期

关键词：

D O I：

10.1006/acha.1996.0017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper minimax rates of convergence for wavelet estimators are studied. The estimators are based on the shrinkage of empirical coefficients <(beta)over cap>(jk) of wavelet decomposition of unknown function with thresholds lambda(j). These thresholds depend on the regularity of the function to be estimated. In the problem of density estimation and nonparametric regression we establish upper rates of convergence over a large range of functional classes and global error measures. The constructed estimate is minimax (up to constant) for all L(pi) error measures, 0 < pi less than or equal to infinity simultaneously. (C) 1996 Academic Press, Inc.

引用

页码：215 / 228

页数：14