A note on wavelet deconvolution density estimation

被引：9
|
作者：
Zeng, Xiaochen [1 ]
机构：
[1] Beijing Univ Technol, Dept Appl Math, Pingle Yuan 100, Beijing 100124, Peoples R China
来源：
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING | 2017年 / 15卷 / 06期
基金：
中国国家自然科学基金; 北京市自然科学基金;
关键词：
Wavelet; density estimation; strong convergence; moderately ill-posed noise; Besov space; STRONG UNIFORM CONSISTENCY; RATES;
D O I：
10.1142/S0219691317500552
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
This paper discusses the uniformly strong convergence of multivariate density estimation with moderately ill-posed noise over a bounded set. We provide a convergence rate over Besov spaces by using a compactly supported wavelet. When the model degenerates to one-dimensional noise-free case, the convergence rate coincides with that of Gine and Nickl's (Ann. Probab., 2009 or Bernoulli, 2010). Our result can also be considered as an extension of Masry's theorem (Stoch. Process. Appl., 1997) to some extent.
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页数：12
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