We study the problem of univariate distribution deconvolution under Wasserstein metrics, with known and ordinary smooth error distributions. We fill a gap present in the literature extending the result on the upper bound rates under Wasserstein metrics for a recently proposed isotone distribution function estimator to the case when the mixing distribution has some level of regularity either in a Holder or in a Sobolev scale. The found rates turn out to be minimax-optimal (up to a logarithmic factor) over the full scale of values of the smoothness index β>0 of the Fourier transform of the error distribution under the 1-Wasserstein distance, while, for Wasserstein metrics of order p>1, these rates are known to be minimax-optimal only for β≤1/2.

Minimax rates for Wasserstein deconvolution of regular distributions with known ordinary smooth errors

Catia Scricciolo
2024-01-01

Abstract

We study the problem of univariate distribution deconvolution under Wasserstein metrics, with known and ordinary smooth error distributions. We fill a gap present in the literature extending the result on the upper bound rates under Wasserstein metrics for a recently proposed isotone distribution function estimator to the case when the mixing distribution has some level of regularity either in a Holder or in a Sobolev scale. The found rates turn out to be minimax-optimal (up to a logarithmic factor) over the full scale of values of the smoothness index β>0 of the Fourier transform of the error distribution under the 1-Wasserstein distance, while, for Wasserstein metrics of order p>1, these rates are known to be minimax-optimal only for β≤1/2.
2024
978-3-031-64430-6
Deconvolution
Minimax rates
Ordinary smooth errors
Wasserstein metrics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1124386
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