# Central limit theorems for eigenvalues in a spiked population model

```@article{Bai2008CentralLT,
title={Central limit theorems for eigenvalues in a spiked population model},
author={Zhidong Bai and Jian-Feng Yao},
journal={Annales De L Institut Henri Poincare-probabilites Et Statistiques},
year={2008},
volume={44},
pages={447-474}
}```
• Published 1 June 2008
• Mathematics
• Annales De L Institut Henri Poincare-probabilites 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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