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Consistent deconvolution in density estimation
Author(s) -
Devroye Luc
Publication year - 1989
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 - 10.2307/3314852
Subject(s) - deconvolution , component (thermodynamics) , almost everywhere , density estimation , construct (python library) , noise (video) , probability density function , mathematics , function (biology) , distribution (mathematics) , statistical physics , physics , combinatorics , mathematical analysis , statistics , computer science , quantum mechanics , artificial intelligence , estimator , biology , evolutionary biology , image (mathematics) , programming language
Suppose we have n observations from X = Y + Z , where Z is a noise component with known distribution, and Y has an unknown density f . When the characteristic function of Z is nonzero almost everywhere, we show that it is possible to construct a density estimate f n such that for all f , Iim n | |=0.