In this paper, we study the problem of estimating a distribution function on ℝ^d, d ≥ 1, from data contaminated by additive noise, using the L^1-distance between distribution functions. We assume that the error distribution is known and belongs to a class of anisotropic ordinary smooth distributions. We derive minimax-optimal convergence rates for L^1-deconvolution in arbitrary dimensions.
Minimax Rates of Convergence for Multivariate Distribution Function L^1-Deconvolution with Known Ordinary Smooth Errors
Catia Scricciolo
2025-01-01
Abstract
In this paper, we study the problem of estimating a distribution function on ℝ^d, d ≥ 1, from data contaminated by additive noise, using the L^1-distance between distribution functions. We assume that the error distribution is known and belongs to a class of anisotropic ordinary smooth distributions. We derive minimax-optimal convergence rates for L^1-deconvolution in arbitrary dimensions.
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