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Adaptive minimax-optimal Wasserstein deconvolution with unknown error distributions

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  • Scricciolo, Catia

Abstract

We study the problem of deconvolving an unknown distribution function when the error distribution is ordinary smooth and unknown. Using data from an auxiliary experiment that provides information about the error distribution, we establish minimax-optimal convergence rates (up to logarithmic factors) with respect to the 1-Wasserstein metric for a kernel-based distribution function estimator over the full range of Hölder-type classes of densities on R. Furthermore, we propose a rate-adaptive, data-driven estimation procedure that automatically selects the optimal bandwidth across α-Hölder-type classes of mixing densities for α≥12, requiring no prior knowledge of the regularity parameters.

Suggested Citation

  • Scricciolo, Catia, 2026. "Adaptive minimax-optimal Wasserstein deconvolution with unknown error distributions," Statistics & Probability Letters, Elsevier, vol. 230(C).
    • Handle: RePEc:eee:stapro:v:230:y:2026:i:c:s0167715225002342
    DOI: 10.1016/j.spl.2025.110589
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    References listed on IDEAS

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    1. Dedecker, Jérôme & Michel, Bertrand, 2013. "Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 278-291.
    2. F. Comte & C. Lacour, 2011. "Data‐driven density estimation in the presence of additive noise with unknown distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 601-627, September.
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