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HIGH-DIMENSIONAL COVARIANCE MATRICES IN ELLIPTICAL DISTRIBUTIONS WITH APPLICATION TO SPHERICAL TEST
Hu, Jiang1,2; Li, Weiming3; Liu, Zhi4; Zhou, Wang5
2019-02
Source PublicationANNALS OF STATISTICS
ISSN0090-5364
Volume47Issue:1Pages:527-555
Abstract

This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among their coordinates, which have great impact on the asymptotic behaviors of linear spectral statistics. Taking such kind of dependency into consideration, we establish a new central limit theorem for the linear spectral statistics in this paper for a class of elliptical populations. This general theoretical result has wide applications and, as an example, it is then applied to test the sphericity of elliptical populations.

KeywordCovariance Matrix High-dimensional Data Elliptical Distribution Sphericity Test
DOI10.1214/18-AOS1699
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000451778700018
PublisherINST MATHEMATICAL STATISTICS
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Northeast Normal Univ, KLASMOE, Changchun 130024, Jilin, Peoples R China;
2.Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China;
3.Shanghai Univ Finance & Econ, Sch Stat & Management, Shanghai 200433, Peoples R China;
4.Univ Macau, Dept Math, Macau, Peoples R China;
5.Natl Univ Singapore, Dept Stat & Appl Probabil, Singapore 117546, Singapore
Recommended Citation
GB/T 7714
Hu, Jiang,Li, Weiming,Liu, Zhi,et al. HIGH-DIMENSIONAL COVARIANCE MATRICES IN ELLIPTICAL DISTRIBUTIONS WITH APPLICATION TO SPHERICAL TEST[J]. ANNALS OF STATISTICS,2019,47(1):527-555.
APA Hu, Jiang,Li, Weiming,Liu, Zhi,&Zhou, Wang.(2019).HIGH-DIMENSIONAL COVARIANCE MATRICES IN ELLIPTICAL DISTRIBUTIONS WITH APPLICATION TO SPHERICAL TEST.ANNALS OF STATISTICS,47(1),527-555.
MLA Hu, Jiang,et al."HIGH-DIMENSIONAL COVARIANCE MATRICES IN ELLIPTICAL DISTRIBUTIONS WITH APPLICATION TO SPHERICAL TEST".ANNALS OF STATISTICS 47.1(2019):527-555.
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