Log-density deconvolution by wavelet thresholding

Bigot, Jérémie [Université Paul Sabatier] Van Bellegem, Sébastien [UCL]

This paper proposes a new wavelet-based method for deconvolving a density. The estimator combines the ideas of nonlinear wavelet thresholding with 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 theoretical 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 practical performance of the estimator, compared with other recently introduced estimators.