Log-density Deconvolution by Wavelet Thresholding

Abstract

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.