Working paper
Log-Density Deconvolution by Wavelet Thresholding
Jérôme Bigot, and Sébastien Van Bellegem
IDEI Working Paper
n. 635, February 11, 2009
Reference
Jérôme Bigot, and Sébastien Van Bellegem, “Log-Density Deconvolution by Wavelet Thresholding”, IDEI Working Paper, n. 635, February 11, 2009.
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;