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

Weiming Li and Jianfeng Yao

Journal of the Royal Statistical Society Series B, 2018, vol. 80, issue 2, 293-318

Abstract: 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 Marčenko–Pastur law. A different and new limit is found and characterized. The reasons for failure of the Marčenko–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.

Date: 2018
References: Add references at CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
https://doi.org/10.1111/rssb.12248

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:80:y:2018:i:2:p:293-318

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868

Access Statistics for this article

Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom

More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().