On structure testing for component covariance matrices of a high dimensional mixture

doi:10.1111/rssb.12248

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	On structure testing for component covariance matrices of a high dimensional mixture
	Li, Weiming 1; Yao, Jianfeng 2
刊名	JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
	2018-03
卷号	80 期号:2 页码:293-318
关键词	Large covariance matrix Marenko-Pastur law Sphericity test
ISSN号	1369-7412
DOI	10.1111/rssb.12248
英文摘要	By studying the family of p-dimensional scale mixtures, the paper shows for the first time a non-trivial example where the eigenvalue distribution of the corresponding sample covariance matrix does not converge to the celebrated Marenko-Pastur law. A different and new limit is found and characterized. The reasons for failure of the Marenko-Pastur limit in this situation are found to be a strong dependence between the p-co-ordinates of the mixture. Next, we address the problem of testing whether the mixture has a spherical covariance matrix. To analyse the traditional John's-type test we establish a novel and general central limit theorem for linear statistics of eigenvalues of the sample covariance matrix. It is shown that John's test and its recent high dimensional extensions both fail for high dimensional mixtures, precisely because of the different spectral limit above. As a remedy, a new test procedure is constructed afterwards for the sphericity hypothesis. This test is then applied to identify the covariance structure in model-based clustering. It is shown that the test has much higher power than the widely used integrated classification likelihood and Bayesian information criteria in detecting non-spherical component covariance matrices of a high dimensional mixture.
WOS研究方向	Mathematics
语种	英语
出版者	WILEY
WOS记录号	WOS:000423371000002
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/692]
专题	上海财经大学
通讯作者	Yao, Jianfeng
作者单位	1.Shanghai Univ Finance & Econ, Shanghai, Peoples R China; 2.Univ Hong Kong, Hong Kong, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Li, Weiming,Yao, Jianfeng. On structure testing for component covariance matrices of a high dimensional mixture[J]. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY,2018,80(2):293-318.
APA	Li, Weiming,&Yao, Jianfeng.(2018).On structure testing for component covariance matrices of a high dimensional mixture.JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY,80(2),293-318.
MLA	Li, Weiming,et al."On structure testing for component covariance matrices of a high dimensional mixture".JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 80.2(2018):293-318.