457 research outputs found
Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one
This paper deals with the estimation of a probability measure on the real
line from data observed with an additive noise. We are interested in rates of
convergence for the Wasserstein metric of order . The distribution of
the errors is assumed to be known and to belong to a class of supersmooth or
ordinary smooth distributions. We obtain in the univariate situation an
improved upper bound in the ordinary smooth case and less restrictive
conditions for the existing bound in the supersmooth one. In the ordinary
smooth case, a lower bound is also provided, and numerical experiments
illustrating the rates of convergence are presented
Uncoupled isotonic regression via minimum Wasserstein deconvolution
Isotonic regression is a standard problem in shape-constrained estimation
where the goal is to estimate an unknown nondecreasing regression function
from independent pairs where . While this problem is well understood both statistically and
computationally, much less is known about its uncoupled counterpart where one
is given only the unordered sets and . In this work, we leverage tools from optimal transport theory to derive
minimax rates under weak moments conditions on and to give an efficient
algorithm achieving optimal rates. Both upper and lower bounds employ
moment-matching arguments that are also pertinent to learning mixtures of
distributions and deconvolution.Comment: To appear in Information and Inference: a Journal of the IM
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