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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
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References:

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