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October 2011 On deconvolution of distribution functions
I. Dattner, A. Goldenshluger, A. Juditsky
Ann. Statist. 39(5): 2477-2501 (October 2011). DOI: 10.1214/11-AOS907


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.


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I. Dattner. A. Goldenshluger. A. Juditsky. "On deconvolution of distribution functions." Ann. Statist. 39 (5) 2477 - 2501, October 2011.


Published: October 2011
First available in Project Euclid: 30 November 2011

zbMATH: 1232.62056
MathSciNet: MR2906875
Digital Object Identifier: 10.1214/11-AOS907

Primary: 62G05 , 62G20

Keywords: Adaptive estimator , Deconvolution , distribution function , minimax risk , rates of convergence

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 5 • October 2011
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