Deconvolution for some singular density errors via a combinatorial median of means approach

摘要

We present a versatile and model based procedure for estimating a density in a decon- volution 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 L~1 loss. We specify them when the density is piecewise constant on a finit enumbe ro f(unknown )pieces ,whe ni ti suni- modal, and when it is concave/convex.