Bounds in $L^1$ Wasserstein distance on the normal approximation of general M-estimators
Statistics Theory
2021-11-19 v1 Statistics Theory
Abstract
We derive quantitative bounds on the rate of convergence in Wasserstein distance of general M-estimators, with an almost sharp (up to a logarithmic term) behavior in the number of observations. We focus on situations where the estimator does not have an explicit expression as a function of the data. The general method may be applied even in situations where the observations are not independent. Our main application is a rate of convergence for cross validation estimation of covariance parameters of Gaussian processes.
Keywords
Cite
@article{arxiv.2111.09721,
title = {Bounds in $L^1$ Wasserstein distance on the normal approximation of general M-estimators},
author = {François Bachoc and Max Fathi},
journal= {arXiv preprint arXiv:2111.09721},
year = {2021}
}