Nonlinear wavelet density estimation for biased data in Sobolev spaces

被引：45

作者：

Wang, Jinru ^{[1
]}

Wang, Meng ^{[1
]}

Zhou, Yuan ^{[1
]}

机构：

[1] Beijing Univ Technol, Dept Appl Math, Beijing 100124, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2013年

基金：

中国国家自然科学基金;

关键词：

Sobolev spaces; wavelet density estimation; hard thresholding; convergence rate;

D O I：

10.1186/1029-242X-2013-308

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the density estimation problem from independent and identically distributed (i.i.d.) biased observations. We develop an adaptive wavelet hard thresholding rule and evaluate its performance by considering risk over Sobolev balls. We prove that our estimation attains a sharp rate of convergence and show the optimality. MSC: 49K40, 90C29, 90C31.

引用

页码：1 / 15

页数：15

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