A mollifier approach to the deconvolution of probability densities

Thorsten Hohage, Pierre Maréchal, Leopold Simar and Anne Vanhems

No 2022011, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: We use mollification to regularize the problem of deconvolution of random variables. This regularization method offers a unifying and generalizing framework in order to compare the benefits of various filter-type techniques like deconvolution kernels, Tikhonov or spectral cut- off methods. In particular, the mollifier approach allows to relax some restrictive assumptions required for the deconvolution kernels, and has better stabilizing properties compared to spectral cutoff or Tikhonov. We show that this approach achieves optimal rates of convergence both for finitely and infinitely smoothing convolution operators under Besov and Sobolev smoothness assumptions on the unknown probability density. The qualification can be arbitrarily high depending on the choice of the mollifier function. We propose an adaptive choice of the regularization parameter using the Lepskii method and we provide simulations to compare the finite sample properties of our estimator with respect to the well-known regularization methods.

Keywords: Deconvolution; nonparametric estimation; inverse problems; regularization; mollification (search for similar items in EconPapers)
Pages: 38
Date: 2022-03-11
New Economics Papers: this item is included in nep-dcm
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Related works:
Journal Article: A MOLLIFIER APPROACH TO THE DECONVOLUTION OF PROBABILITY DENSITIES (2024)
Working Paper: A mollifier approach to the deconvolution of probability densities (2022)
Working Paper: A mollifier approach to the deconvolution of probability densities (2018)
Working Paper: A mollifier approach to the deconvolution of probability densities (2018)
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