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 H\"older-type classes of densities on $\mathbb{R}$. Furthermore, we propose a rate-adaptive, data-driven estimation procedure that automatically selects the optimal bandwidth across $\alpha$-H\"older-type classes of mixing densities for $\alpha\geq\frac{1}{2}$, requiring no prior knowledge of the regularity parameters.
Adaptive minimax-optimal Wasserstein deconvolution with unknown error distributions
Catia Scricciolo
2026-01-01
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 H\"older-type classes of densities on $\mathbb{R}$. Furthermore, we propose a rate-adaptive, data-driven estimation procedure that automatically selects the optimal bandwidth across $\alpha$-H\"older-type classes of mixing densities for $\alpha\geq\frac{1}{2}$, requiring no prior knowledge of the regularity parameters.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
