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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\u012d method, and we provide simulations to compare the finite sample properties of our estimator with respect to the well-known regularization methods.<\/jats:p>","DOI":"10.1017\/s0266466622000457","type":"journal-article","created":{"date-parts":[[2022,10,28]],"date-time":"2022-10-28T07:04:49Z","timestamp":1666940689000},"page":"320-359","source":"Crossref","is-referenced-by-count":4,"title":["A MOLLIFIER APPROACH TO THE DECONVOLUTION OF PROBABILITY DENSITIES"],"prefix":"10.1017","volume":"40","author":[{"given":"Thorsten","family":"Hohage","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre","family":"Mar\u00e9chal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L\u00e9opold","family":"Simar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anne","family":"Vanhems","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2022,10,28]]},"reference":[{"key":"S0266466622000457_r23","doi-asserted-by":"publisher","DOI":"10.1214\/009053607000000028"},{"key":"S0266466622000457_r28","doi-asserted-by":"publisher","DOI":"10.1080\/09500348714550241"},{"key":"S0266466622000457_r16","doi-asserted-by":"publisher","DOI":"10.2307\/3314852"},{"key":"S0266466622000457_r30","doi-asserted-by":"publisher","DOI":"10.1137\/1136085"},{"key":"S0266466622000457_r29","doi-asserted-by":"publisher","DOI":"10.1137\/1135065"},{"key":"S0266466622000457_r7","doi-asserted-by":"publisher","DOI":"10.1017\/S026646661000040X"},{"key":"S0266466622000457_r14","doi-asserted-by":"publisher","DOI":"10.1214\/009053607000000884"},{"key":"S0266466622000457_r32","doi-asserted-by":"publisher","DOI":"10.3150\/15-BEJ763"},{"key":"S0266466622000457_r35","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139994264476"},{"key":"S0266466622000457_r44","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1017939249"},{"key":"S0266466622000457_r46","volume-title":"Real and Complex Analysis: Part 2","author":"Rudin","year":"1970"},{"key":"S0266466622000457_r2","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2011.01.016"},{"key":"S0266466622000457_r11","doi-asserted-by":"publisher","DOI":"10.1002\/cjs.5550340305"},{"key":"S0266466622000457_r36","doi-asserted-by":"publisher","DOI":"10.1109\/23.873021"},{"key":"S0266466622000457_r21","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1944-0009701-0"},{"key":"S0266466622000457_r4","first-page":"97","article-title":"A variational approach to the inversion of some compact operators","volume":"5","author":"Bonnefond","year":"2009","journal-title":"Pacific Journal of Optimization"},{"key":"S0266466622000457_r12","doi-asserted-by":"publisher","DOI":"10.1080\/10629360600831711"},{"key":"S0266466622000457_r18","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-1740-8"},{"key":"S0266466622000457_r40","doi-asserted-by":"publisher","DOI":"10.1137\/0310009"},{"key":"S0266466622000457_r48","doi-asserted-by":"publisher","DOI":"10.1080\/02331889008802238"},{"key":"S0266466622000457_r51","doi-asserted-by":"publisher","DOI":"10.1007\/s10013-015-0119-1"},{"key":"S0266466622000457_r52","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-3222-0_51"},{"key":"S0266466622000457_r53","unstructured":"Wikipedia Contributors (2020) Mollifier\u2014Wikipedia, the free encyclopedia (Online; 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