Deconvolution for some singular density errors via a combinatorial median of means approach
Clément Marteau
Université Claude Bernard Lyon 1, Villeurbanne, FranceMathieu Sart
Université Jean Monnet Saint-Étienne, France
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Abstract
We present a versatile and model based procedure for estimating a density in a deconvolution setting where the error density is assumed to be singular enough.We assess the quality of our estimator by establishing non-asymptotic risk bounds for the loss. We specify them when the density is piecewise constant on a finite number of (unknown) pieces, when it is unimodal, and when it is concave/convex.
Cite this article
Clément Marteau, Mathieu Sart, Deconvolution for some singular density errors via a combinatorial median of means approach. Math. Stat. Learn. 6 (2023), no. 1/2, pp. 51–85
DOI 10.4171/MSL/36