Robust Estimates of Covariance Matrices in Large Dimensional Regime

Abstract : This paper studies the limiting behavior of a class of robust population covariance matrix estimators, originally due to Maronna in 1976, in the regime where both the number of available samples and the population size grow large. Using tools from random matrix theory, we prove that, for sample vectors made of independent entries having some moment conditions, the difference between the sample covariance matrix and (a scaled version of) such robust estimator tends to zero in spectral norm, almost surely. This result can be applied to various statistical methods arising from random matrix theory that can be made robust without altering their first order behavior.
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Article dans une revue
IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2014, 60 (11), pp.7269 - 7278. 〈10.1109/TIT.2014.2354045〉
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Contributeur : Virginie Bouvier <>
Soumis le : jeudi 15 janvier 2015 - 18:06:20
Dernière modification le : jeudi 9 février 2017 - 15:34:58

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Romain Couillet, Frédéric Pascal, Jack W. Silverstein. Robust Estimates of Covariance Matrices in Large Dimensional Regime. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2014, 60 (11), pp.7269 - 7278. 〈10.1109/TIT.2014.2354045〉. 〈hal-01104000〉

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