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.
Funding Statement
This work was supported by the Projects MESA (ANR-18-CE40-006) and GAP (ANR-21-CE40-0007) of the French National Research Agency (ANR).
Acknowledgments
We are grateful to the editorial team for their comments that led to an improvement of this manuscript.
Citation
François Bachoc. Max Fathi. "Bounds in Wasserstein distance on the normal approximation of general M-estimators." Electron. J. Statist. 17 (1) 1457 - 1491, 2023. https://doi.org/10.1214/23-EJS2132
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