On Catoni's M-Estimation

10/15/2022

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Catoni proposed a robust M-estimator and gave the deviation inequality for one fixed test function. The present paper is devoted to the uniform concentration inequality for a family of test functions. As an application, we consider empirical risk minimization for heavy-tailed losses.

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On Catoni's M-Estimation

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On Catoni's M-Estimation

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Variations and extensions of the Gaussian concentration inequality, Part II

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Estimation of the weighted integrated square error of the Grenander estimator by the Kolmogorov-Smirnov statistic

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