Joint density of eigenvalues in spiked multivariate models

Abstract

The classical methods of multivariate analysis are based on the eigenvalues of one or two sample covariance matrices. In many applications of these methods, for example to high dimensional data, it is natural to consider alternative hypotheses which are a low rank departure from the null hypothesis. For rank one alternatives, this note provides a representation for the joint eigenvalue density in terms of a single contour integral. This will be of use for deriving approximate distributions for likelihood ratios and linear statistics used in testing.

References in corpus (6)

• Asymptotic power of sphericity tests for high-dimensional data
• The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, part I
• Probability densities and distributions for spiked and general variance Wishart $\beta$-ensembles
• Three Problems Related to the Eigenvalues of Complex Non-central Wishart Matrices with a Rank-1 Mean
• A note on the CLT of the LSS for sample covariance matrix from a spiked population model
• Roy's Largest Root Test Under Rank-One Alternatives

Cited by in corpus (1)

• Hypergeometric Functions of Matrix Arguments and Linear Statistics of Multi-Spiked Hermitian Matrix Models