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Tests for high-dimensional covariance matrices using the theory of U-statistics
Uppsala University, Sweden; Swedish University of Agriculture Science, Sweden; University of Munich, Germany.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Swedish University of Agriculture Science, Sweden.
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 and#8811;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
Taylor and Francis: STM, Behavioural Science and Public Health Titles , 2015. Vol. 85, no 13, 2619-2631 p.
Keyword [en]
covariance testing; U-statistics; high-dimensional data; sphericity
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-119781DOI: 10.1080/00949655.2014.948441ISI: 000355538300006OAI: oai:DiVA.org:liu-119781DiVA: diva2:827293
Note

Funding Agencies|DAAD (German Academic Exchange Service)

Available from: 2015-06-26 Created: 2015-06-26 Last updated: 2015-06-26

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