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Penalized contrast estimator for adaptive density deconvolution
Author(s) -
Comte Fabienne,
Rozenholc Yves,
Taupin MarieLuce
Publication year - 2006
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.5550340305
Subject(s) - independent and identically distributed random variables , estimator , adaptive estimator , minimax , minimax estimator , mathematics , contrast (vision) , deconvolution , rate of convergence , statistics , mathematical optimization , algorithm , computer science , random variable , minimum variance unbiased estimator , artificial intelligence , computer network , channel (broadcasting)
The authors consider the problem of estimating the density g of independent and identically distributed variables X I , from a sample Z 1 ,… Z n such that Z I = X I + σϵ for i = 1,…, n, and E is noise independent of X, with σϵ having a known distribution. They present a model selection procedure allowing one to construct an adaptive estimator of g and to find nonasymptotic risk bounds. The estimator achieves the minimax rate of convergence, in most cases where lower bounds are available. A simulation study gives an illustration of the good practical performance of the method.