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Tests for high-dimensional covariance matrices using the theory of U-statistics
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
2015 (English)In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 85, no 13, 2619-2631 p.Article in journal (Refereed) Published
Abstract [en]

Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Under certain mild conditions mainly on the traces of the unknown covariance matrix, and using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. A real data set is used to illustrate the application of the proposed test statistics.

Place, publisher, year, edition, pages
2015. Vol. 85, no 13, 2619-2631 p.
Keyword [en]
covariance testing, U-statistics, high-dimensional data, sphericity
National Category
Probability Theory and Statistics
URN: urn:nbn:se:uu:diva-256978DOI: 10.1080/00949655.2014.948441ISI: 000355538300006OAI: oai:DiVA.org:uu-256978DiVA: diva2:827973
Available from: 2015-06-29 Created: 2015-06-29 Last updated: 2015-06-29Bibliographically approved

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Ahmad, M. Rauf
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