Limiting laws for extreme eigenvalues of large-dimensional spiked Fisher matrices with a divergent number of spikes

Junshan Xie, Yicheng Zeng, Lixing ZHU*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Consider the p×p matrix that is the product of a population covariance matrix and the inverse of another population covariance matrix. Suppose that their difference has a divergent rank with respect to p, when two samples of sizes n and T from the two populations are available, we construct its corresponding sample version. In the high-dimensional regime where both n and T are proportional to p, we investigate the limiting laws for extreme (spiked) eigenvalues of the sample (spiked) Fisher matrix when the number of spikes is divergent and these spikes are unbounded. We derive the convergence in probability of these spiked eigenvalues after scaling, and the central limit theorem for normalized spiked eigenvalues.

Original languageEnglish
Article number104742
JournalJournal of Multivariate Analysis
Volume184
DOIs
Publication statusPublished - Jul 2021

Scopus Subject Areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Extreme eigenvalue
  • Fisher matrix
  • Phase transition phenomenon
  • Random matrix theory
  • Spiked population model

Fingerprint

Dive into the research topics of 'Limiting laws for extreme eigenvalues of large-dimensional spiked Fisher matrices with a divergent number of spikes'. Together they form a unique fingerprint.

Cite this