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A mollifier approach to the deconvolution of probability densities

Maréchal, Pierre, Simar, Léopold and Vanhems, Anne (2018) A mollifier approach to the deconvolution of probability densities. TSE Working Paper, n. 18-965, Toulouse

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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.

Item Type: Monograph (Working Paper)
Language: English
Date: November 2018
Place of Publication: Toulouse
Divisions: TSE-R (Toulouse)
Institution: Toulouse Capitole University
Site: UT1
Date Deposited: 19 Nov 2018 11:33
Last Modified: 04 Apr 2019 04:21
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