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

11/18/2021

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by   François Bachoc, et al.

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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.