A mollifier approach to the deconvolution of probability densities

Pierre Maréchal (Institut de Mathématiques de Toulouse - Université Paul Sabatier)

April 16, 2019, 15:30–17:00

Room MS001

Econometrics and Empirical Economics Seminar


In this paper, we use a mollifier approach to regularize the deconvolution, which has been used in research fields like medical imaging, tomography, astrophysics but, to the best of our knowledge, never in statistics or econometrics. We show that the analysis of this new regularization method offers a unifying and generalizing frame in order to compare the benefits of various different filter-type techniques like deconvolution kernels, Tikhonov or spectral cut-off method. In particular, the mollifier approach allows to relax some restrictive assumptions required for the deconvolution problem, and has better stabilizing properties compared to spectral cutoff and Tikhonov. We prove the asymptotic convergence of our estimator and provide simulations analysis to compare the finite sample properties of our estimator with respect to the well-known methods.