ON DECONVOLUTION OF DISTRIBUTION FUNCTIONS

被引：39

作者：

Dattner, I. ^{[1
]}

Goldenshluger, A. ^{[1
]}

Juditsky, A. ^{[2
]}

机构：

[1] Univ Haifa, Dept Stat, IL-31905 Haifa, Israel

[2] Univ Grenoble 1, LMC, F-38041 Grenoble 9, France

来源：

ANNALS OF STATISTICS | 2011年 / 39卷 / 05期

关键词：

Adaptive estimator; deconvolution; minimax risk; rates of convergence; distribution function; LINEAR FUNCTIONALS; NONPARAMETRIC-ESTIMATION; DENSITY DECONVOLUTION; ADAPTIVE ESTIMATION; GEOMETRIZING RATES; SHARP OPTIMALITY; CONVERGENCE; CONVOLUTION;

D O I：

10.1214/11-AOS907

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：

The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density belonging to the Sobolev class, and the error density is ordinary smooth. We develop rate optimal estimators based on direct inversion of empirical characteristic function. We also derive minimax affine estimators of the distribution function which are given by an explicit convex optimization problem. Adaptive versions of these estimators are proposed, and some numerical results demonstrating good practical behavior of the developed procedures are presented.

引用

页码：2477 / 2501

页数：25

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