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arXiv · 2111.09721

Bounds in $L^1$ Wasserstein distance on the normal approximation of general M-estimators

François Bachoc·Max Fathi
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Abstract

We derive quantitative bounds on the rate of convergence in $L^1$ 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.

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François Bachoc, Max Fathi. 2021-11-18. Bounds in $L^1$ Wasserstein distance on the normal approximation of general M-estimators. https://arxiv.org/abs/2111.09721

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