Eigenvalues of Large Sample Covariance Matrices of Spiked Population Models

TL;DR

This paper analyzes the behavior of sample eigenvalues in large spiked covariance models, establishing their almost sure limits as both sample and population sizes grow large, providing insights into high-dimensional covariance estimation.

Contribution

It precisely characterizes the almost sure limits of sample eigenvalues in large spiked models, extending understanding of eigenvalue behavior in high-dimensional settings.

Findings

Almost sure limits for sample eigenvalues are derived.

Results apply to a broad class of sample distributions.

Provides theoretical foundation for high-dimensional covariance analysis.

Abstract

We consider a spiked population model, proposed by Johnstone, whose population eigenvalues are all unit except for a few fixed eigenvalues. The question is to determine how the sample eigenvalues depend on the non-unit population ones when both sample size and population size become large. This paper completely determines the almost sure limits for a general class of samples.