ON DECONVOLUTION OF DISTRIBUTION FUNCTIONS

• 成果类型: Article
• 署名作者: Dattner, I.; Goldenshluger, A.; Juditsky, A.
• 署名单位: University of Haifa; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS907
• 发表日期: 2011
• 页码: 2477-2501
• 关键词: linear functionals; nonparametric-estimation; density deconvolution; Adaptive estimation; geometrizing rates; sharp optimality; CONVERGENCE; convolution

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.