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

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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Journal articles
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https://hal.archives-ouvertes.fr/hal-00794107
Contributor : Bertrand Michel <>
Submitted on : Monday, February 25, 2013 - 10:59:21 PM
Last modification on : Friday, September 20, 2019 - 4:34:03 PM
Long-term archiving on: Sunday, May 26, 2013 - 9:20:07 AM

### Files

optimalWfinal.pdf
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### Identifiers

• HAL Id : hal-00794107, version 2
• ARXIV : 1302.6103

### Citation

Jérôme Dedecker, Bertrand Michel. Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension. Journal of Multivariate Analysis, Elsevier, 2013. ⟨hal-00794107v2⟩

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