Asymptotic Normality of the Largest Eigenvalue for Noncentral Sample Covariance Matrices

2024/10/22 by Cheng, Huihui, Song, Minjie
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2410.17085

Abstract

Let X be a p× n independent identically distributed real Gaussian matrix with positive mean μ and variance σ² entries. The goal of this paper is to investigate the largest eigenvalue of the noncentral sample covariance matrix W=XX^T/n, when the dimension p and the sample size n both grow to infinity with the limit p/n=c (0

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