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.


62J10 Analysis of variance and covariance (ANOVA)
62G35 Nonparametric robustness
62G15 Nonparametric tolerance and confidence regions
Full Text: DOI arXiv Euclid


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