Spiked sample covariance matrices with possibly multiple bulk components

TL;DR

This paper investigates the spectral behavior of spiked sample covariance matrices with multiple bulk components, extending Johnstone's model, and provides results on eigenvalue and eigenvector convergence to support advanced statistical applications.

Contribution

It introduces an extended model for spiked covariance matrices with multiple bulk components and analyzes their eigenvalue and eigenvector limits and rates.

Findings

Eigenvalues converge to specific limits with quantifiable rates.

Eigenvectors exhibit predictable asymptotic behavior.

Results enable extensions of statistical methods based on the model.

Abstract

In this paper, we study the convergent limits and rates of the eigenvalues and eigenvectors for spiked sample covariance matrices whose spectrum can have multiple bulk components. Our model is an extension of Johnstone's spiked covariance matrix model. Based on our results, we can extend many statistical applications based on Johnstone's spiked covariance matrix model.