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Deconvolution of supersmooth densities with smooth noise
Author(s) -
Butucea Cristina
Publication year - 2004
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 - 10.2307/3315941
Subject(s) - independent and identically distributed random variables , estimator , mathematics , pointwise , deconvolution , kernel density estimation , random variable , minimax , probability density function , rate of convergence , context (archaeology) , statistics , mathematical optimization , mathematical analysis , computer science , channel (broadcasting) , computer network , paleontology , biology
The author considers the estimation of the common probability density of independent and identically distributed random variables observed with added white noise. She assumes that the unknown density belongs to some class of supersmooth functions, and that the error distribution is ordinarily smooth, meaning that its characteristic function decays polynomially asymptotically. In this context, the author evaluates the minimax rate of convergence of the pointwise risk and describes a kernel estimator having this rate. She computes upper bounds for the L 2 risk of this estimator.