Eigenvalues of large sample covariance matrices of spiked population models

Authors:
Jinho Baik;Jack W. Silverstein
Affiliations:
Department of Mathematics, University of Michigan, Ann Arbor, MI;Department of Mathematics, North Carolina State University, Raleigh, NC
Venue:
Journal of Multivariate Analysis
Year:
2006

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Abstract

We consider a spiked population model, proposed by Johnstone, in which all the population eigenvalues are one except for a few fixed eigenvalues. The question is to determine how the sample eigenvalues depend on the non-unit population ones when both sample size and population size become large. This paper completely determines the almost sure limits of the sample eigenvalues in a spiked model for a general class of samples.