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We study the problem of univariate distribution function 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 Hölder 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 \(\beta >0\) 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 \(\beta \le \frac{1}{2}\) .

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Minimax Rates for Wasserstein Deconvolution of Regular Distributions with Known Ordinary Smooth Errors

  • 会议论文

  • 发表日期：

    2025年

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  • Catia Scricciolo

摘要

We study the problem of univariate distribution function 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 Hölder 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 \(\beta >0\) 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 \(\beta \le \frac{1}{2}\) .