Robust multivariate mean estimation: the optimality of trimmed mean

Gabor Lugosi; Shahar Mendelson

Robust multivariate mean estimation: the optimality of trimmed mean

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arxiv 1907.11391 v2 pith:W23XPIHA submitted 2019-07-26 math.ST stat.TH

Gabor Lugosi , Shahar Mendelson This is my paper · ORCID

classification math.STstat.TH

keywords meanmultivariateadversarialconditionsconsidercontaminationestimatingestimation

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We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal conditions.

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Lecture Notes: Selected topics on robust statistical learning theory
stat.ML 2019-08 conditional novelty 3.0 of 10

These lecture notes synthesize robust statistical learning theory, showing how median-of-means, minimax, homogeneity, and small-ball principles yield oracle inequalities for both ERM and robust estimators.

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