A note on the CLT of the LSS for sample covariance matrix from a spiked population model

Abstract

In this note, we establish an asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance structure. As an application, we provide an asymptotic power function for the corrected likelihood ratio statistic for testing the presence of spike eigenvalues in the population covariance matrix. This result generalizes an existing formula from the literature where only one simple spike exists.

18 pages, 4 figures

Cited by in corpus (4)

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• Hypergeometric Functions of Matrix Arguments and Linear Statistics of Multi-Spiked Hermitian Matrix Models
• Joint density of eigenvalues in spiked multivariate models
• On estimation of the noise variance in high-dimensional probabilistic principal component analysis