On deconvolution of distribution functions
I. Dattner, A. Goldenshluger, A. Juditsky
The Annals of Statistics · 2011 · Volume 39 · Issue 5
Abstract
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.
Keywords
62G05, 62G20, Adaptive estimator, Deconvolution, distribution function, minimax risk, rates of convergence
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