## Robust covariance estimation under $$L_4$$-$$L_2$$ norm equivalence.(English)Zbl 1451.62084

This paper proposes and evaluates estimators of covariance matrices. Concepts of sub-Gaussian random vectors, bounded kurtosis, strong and weak norms, weak variance and effective rank are developed. For a random vector $$X$$ satisfying a bounded kurtosis assumption, a covariance estimation procedure is proposed that performs, in terms of the accuracy/confidence tradeoff, as if $$X$$ is a Gaussian vector. The bounds explicited for the estimation error do not depend on the dimension of the vector.

### MSC:

 62J10 Analysis of variance and covariance (ANOVA) 62G35 Nonparametric robustness 62G15 Nonparametric tolerance and confidence regions

### Keywords:

covariance estimation; robust estimation; median of means
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### References:

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