The largest eigenvalues of sample covariance matrices for a spiked population: Diagonal case

Delphine Féral, Sandrine Péché

Type: Article

Publication Date: 2009-07-01

Citations: 41

DOI: https://doi.org/10.1063/1.3155785

Abstract

We consider large complex random sample covariance matrices obtained from "spiked populations", that is when the true covariance matrix is diagonal with all but finitely many eigenvalues equal to one. We investigate the limiting behavior of the largest eigenvalues when the population and the sample sizes both become large. Under some conditions on moments of the sample distribution, we prove that the asymptotic fluctuations of the largest eigenvalues are the same as for a complex Gaussian sample with the same true covariance. The real setting is also considered.

Locations

Journal of Mathematical Physics - View
arXiv (Cornell University) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF
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