Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings

Tony Cai, Weidong Liu and Yin Xia

Journal of the American Statistical Association, 2013, vol. 108, issue 501, 265-277

Abstract: In the high-dimensional setting, this article considers three interrelated problems: (a) testing the equality of two covariance matrices and ; (b) recovering the support of ; and (c) testing the equality of and row by row. We propose a new test for testing the hypothesis H 0 : and investigate its theoretical and numerical properties. The limiting null distribution of the test statistic is derived and the power of the test is studied. The test is shown to enjoy certain optimality and to be especially powerful against sparse alternatives. The simulation results show that the test significantly outperforms the existing methods both in terms of size and power. Analysis of a prostate cancer dataset is carried out to demonstrate the application of the testing procedures. When the null hypothesis of equal covariance matrices is rejected, it is often of significant interest to further investigate how they differ from each other. Motivated by applications in genomics, we also consider recovering the support of and testing the equality of the two covariance matrices row by row. New procedures are introduced and their properties are studied. Applications to gene selection are also discussed. Supplementary materials for this article are available online.

Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (38)

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2012.758041 (text/html)
Access to full text is restricted to subscribers.

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:taf:jnlasa:v:108:y:2013:i:501:p:265-277

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2012.758041

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().