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 Asymptotic Linear Spectral Statistics for Spiked Hermitian Random Matrices Damien Passemier1; Matthew R. McKay1; Yang Chen2 2015-03-24 Source Publication Journal of Statistical Physics ISSN 0022-4715 Volume 160Issue: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. Keyword F-matrix High-dimensional Statistics Hypothesis Testing Mimo Systems Random Matrix Theory Spiked Population Model Wishart Ensembles DOI 10.1007/s10955-015-1233-x URL View the original Indexed By SCI Language 英语 WOS Research Area Physics WOS Subject Physics, Mathematical WOS ID WOS:000356579000007 Fulltext Access Citation statistics Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS] Document Type Journal article Collection DEPARTMENT OF MATHEMATICS Affiliation 1.Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Clear Water Bay, Kowloon, Hong Kong2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Avenue Padre Tomás Pereira, Taipa, Macau, China Recommended CitationGB/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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