A mollifier approach to the deconvolution of probability densities

Thorsten Hohage, Pierre Maréchal, Leopold Simar and Anne Vanhems

No 2022041, LIDAM Reprints 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 cutoff methods. In particular, the mollifier approach allows to relax some restrictive assumptions required for the deconvolution kernels, and has better stabilizing properties compared with spectral cutoff or Tikhonov. We show that this approach achieves optimal rates of convergence for both 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 Lepski ̆ı method, and we provide simulations to compare the finite sample properties of our estimator with respect to the well-known regularization methods.

Pages: 40
Date: 2022-10-28
Note: In: Econometric Theory, 2022
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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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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2022041

DOI: 10.1017/S0266466622000457

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