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Article Dans Une Revue Journal of Multivariate Analysis Année : 2013

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

Résumé

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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Dates et versions

hal-00794107 , version 1 (25-02-2013)
hal-00794107 , version 2 (25-02-2013)

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Citer

Jérôme Dedecker, Bertrand Michel. Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension. Journal of Multivariate Analysis, 2013, 122. ⟨hal-00794107v2⟩
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