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Log‐density Deconvolution by Wavelet Thresholding
Author(s) -
BIGOT JÉRÉMIE,
BELLEGEM SÉBASTIEN VAN
Publication year - 2009
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2009.00653.x
Subject(s) - mathematics , estimator , wavelet , deconvolution , density estimation , thresholding , projection (relational algebra) , besov space , rate of convergence , mathematical optimization , statistics , algorithm , artificial intelligence , image (mathematics) , computer science , computer network , biochemistry , chemistry , channel (broadcasting) , functional analysis , interpolation space , gene
. This paper proposes a new wavelet‐based method for deconvolving a density. The estimator combines the ideas of non‐linear wavelet thresholding with periodized Meyer wavelets and estimation by information projection. It is guaranteed to be in the class of density functions, in particular it is positive everywhere by construction. The asymptotic optimality of the estimator is established in terms of the rate of convergence of the Kullback–Leibler discrepancy over Besov classes. Finite sample properties are investigated in detail, and show the excellent empirical performance of the estimator, compared with other recently introduced estimators.