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Eigenvalues of large sample covariance matrices of spiked population models. (English) Zbl 1220.15011
Authors’ 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.”

MSC:
15A18Eigenvalues, singular values, and eigenvectors
15B52Random matrices
60F17Functional limit theorems; invariance principles
62P20Applications of statistics to economics
62H99Multivariate analysis
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References:
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