Deconvolution for some singular density errors with respect to the $\mathbb{L}^1$ loss

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 $\mathbb{L}^1$ loss. We specify them under various...

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Bibliographic Details
Published in:Mathematical statistics and learning (Online) 2022-12, Vol.6 (1), p.51-85
Main Authors: Marteau, Clément, Sart, Mathieu
Format: Article
Language:English
Subjects:
Mathematics
Statistics
Online Access:Get full text
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Summary: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 $\mathbb{L}^1$ loss. We specify them under various constraints on the target. We investigate cases where the density is multimodal, (piecewise) concave/convex, belongs to a (possibly inhomogeneous) Besov space or a particular parametric model. Moreover, our estimation procedure is robust with respect to model misspecification.
ISSN:2520-2316
2520-2324
DOI:10.4171/MSL/36