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Title: Central limit theorems for eigenvalues in a spiked population model
Authors: Bai, Z. 
Yao, J.-F.
Keywords: Central limit theorems
Extreme eigenvalues
Largest eigenvalue
Random quadratic forms
Random sesquilinear forms
Sample covariance matrices
Spiked population model
Issue Date: Jun-2008
Citation: Bai, Z., Yao, J.-F. (2008-06). Central limit theorems for eigenvalues in a spiked population model. Annales de l'institut Henri Poincare (B) Probability and Statistics 44 (3) : 447-474. ScholarBank@NUS Repository.
Abstract: 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 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. © Association des Publications de l'Institut Henri Poincaré, 2008.
Source Title: Annales de l'institut Henri Poincare (B) Probability and Statistics
ISSN: 02460203
DOI: 10.1214/07-AIHP118
Appears in Collections:Staff Publications

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