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Central limit theorems for eigenvalues in a spiked population model

Zhidong BaiJian-Feng Yao — 2008

Annales de l'I.H.P. Probabilités et statistiques

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with empirical findings on various data sets. The question is to quantify the effect of the perturbation caused by the spike eigenvalues. A recent work by Baik and Silverstein establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the population and the...

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