Working paper

Log-Density Deconvolution by Wavelet Thresholding

Jérôme Bigot, and Sébastien Van Bellegem

Abstract

This paper proposes a new wavelet-based method for deconvolving a density. The estimator combines the ideas of nonlinear wavelet thresholding with periodised 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 rate of convergence of the Kullback-Leibler discrepancy over Besov classes. Finite sample properties is investigated in detail, and show the excellent empirical performance of the estimator, compared with other recently introduced estimators.

Keywords

deconvolution; wavelet thresholding; adaptive estimation;

See also

Published in

TSE Working Paper, n. 09-011, February 11, 2009