On deconvolution of distribution functions

Details On deconvolution of distribution functions On deconvolution of distribution functions

2010-06-20

arxiv.org/abs/1006.3918v2

Annals of Statistics 2011, Vol. 39, No. 5, 2477-2501

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/11-AOS907 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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