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Asymptotic Linear Spectral Statistics for Spiked Hermitian Random Matrices
Damien Passemier1; Matthew R. McKay1; Yang Chen2
2015-03-24
Source PublicationJournal of Statistical Physics
ISSN0022-4715
Volume160Issue:1Pages:120-150
Abstract

Using the Coulomb Fluid method, this paper derives central limit theorems (CLTs) for linear spectral statistics of three “spiked” Hermitian random matrix ensembles. These include Johnstone’s spiked model (i.e., central Wishart with spiked correlation), non-central Wishart with rank-one non-centrality, and a related class of non-central $$F$$F matrices. For a generic linear statistic, we derive simple and explicit CLT expressions as the matrix dimensions grow large. For all three ensembles under consideration, we find that the primary effect of the spike is to introduce an $$O(1)$$O(1) correction term to the asymptotic mean of the linear spectral statistic, which we characterize with simple formulas. The utility of our proposed framework is demonstrated through application to three different linear statistics problems: the classical likelihood ratio test for a population covariance, the capacity analysis of multi-antenna wireless communication systems with a line-of-sight transmission path, and a classical multiple sample significance testing problem.

KeywordF-matrix High-dimensional Statistics Hypothesis Testing Mimo Systems Random Matrix Theory Spiked Population Model Wishart Ensembles
DOI10.1007/s10955-015-1233-x
URLView the original
Indexed BySCI
Language英语
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000356579000007
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Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Clear Water Bay, Kowloon, Hong Kong
2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Avenue Padre Tomás Pereira, Taipa, Macau, China
Recommended Citation
GB/T 7714
Damien Passemier,Matthew R. McKay,Yang Chen. Asymptotic Linear Spectral Statistics for Spiked Hermitian Random Matrices[J]. Journal of Statistical Physics,2015,160(1):120-150.
APA Damien Passemier,Matthew R. McKay,&Yang Chen.(2015).Asymptotic Linear Spectral Statistics for Spiked Hermitian Random Matrices.Journal of Statistical Physics,160(1),120-150.
MLA Damien Passemier,et al."Asymptotic Linear Spectral Statistics for Spiked Hermitian Random Matrices".Journal of Statistical Physics 160.1(2015):120-150.
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