TY - JOUR
T1 - Limiting laws for extreme eigenvalues of large-dimensional spiked Fisher matrices with a divergent number of spikes
AU - Xie, Junshan
AU - Zeng, Yicheng
AU - ZHU, Lixing
N1 - Funding Information:
The authors gratefully acknowledge a grant from the University Grants Council of Hong Kong and a NSFC, China grant (NSFC11671042). Drs Xie and Zeng are co-first authors. Zeng and Zhu are in charge of all revisions. The authors thank Editor, Associate editor and two referees for their constructive comments and suggestions that led to an improvement of the early manuscript.
PY - 2021/7
Y1 - 2021/7
N2 - 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.
AB - 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.
KW - Extreme eigenvalue
KW - Fisher matrix
KW - Phase transition phenomenon
KW - Random matrix theory
KW - Spiked population model
UR - http://www.scopus.com/inward/record.url?scp=85103011196&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2021.104742
DO - 10.1016/j.jmva.2021.104742
M3 - Article
AN - SCOPUS:85103011196
SN - 0047-259X
VL - 184
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
M1 - 104742
ER -