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arXiv · 1302.6103

Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension

Jérôme Dedecker·Bertrand Michel
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Abstract

The subject of this paper is the estimation of a probability measure on ${\mathbb R}^d$ from data observed with an additive noise, under the Wasserstein metric of order $p$ (with $p\geq 1$). We assume that the distribution of the errors is known and belongs to a class of supersmooth distributions, and we give optimal rates of convergence for the Wasserstein metric of order $p$. In particular, we show how to use the existing lower bounds for the estimation of the cumulative distribution function in dimension one to find lower bounds for the Wasserstein deconvolution in any dimension.

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Jérôme Dedecker, Bertrand Michel. 2013-02-25. Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension. https://arxiv.org/abs/1302.6103

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