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Pré-Publication, Document De Travail Année : 2021

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

Résumé

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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Dates et versions

hal-03432921 , version 1 (17-11-2021)

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François Bachoc, Max Fathi. Bounds in $L^1$ Wasserstein distance on the normal approximation of general M-estimators. 2021. ⟨hal-03432921⟩
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