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Annales de l'Institut Henri Poincare (B) Probability and Statistics 44, 3 (2008) 447-474

Central limit theorems for eigenvalues in a spiked population model

Zhidong Bai 1, 2, Jian-Feng Yao 3

(2008)

In a spiked population model, the population covariance matrix has all its eigenvalues equal to unit 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 sample sizes become large. This paper establishes the limiting distributions of these extreme sample eigenvalues. As another important result of the paper, we provide a central limit theorem on random sesquilinear forms.

1:	Key Laboratory of Applied Statistics under Ministry of Education (KLASMOE)
	Northeast Normal University
2:	Department of Statistics and Applied Probability (DSAP)
	National University of Singapore
3:	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne

Subject

:

Mathematics/Statistics Statistics/Statistics Theory Mathematics/Probability

Keyword(s): Sample covariance matrices – Spiked population model – Central limit theorems – Largest eigenvalue – Extreme eigenvalues – Random sesquilinear forms – Random quadratic forms

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From: Jian-Feng Yao <>

Submitted on: Tuesday, 6 February 2007 18:21:52

Updated on: Thursday, 4 February 2010 15:23:47