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Some Tests of Covariance Matrices for High Dimensional Multivariate Data
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.ORCID iD: 0000-0001-9896-4438
Department of Energy and Technology, Swedish Univerity of Agricultural Sciences, SE-750 07 Uppsala, Sweden.
2011 (English)Report (Other academic)
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. 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 statistics are derived under very general conditions, particularly avoiding any strict assumptions on the traces of the unknown covariance matrix. Neither any relationship between n and p is assumed. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. The validity of the commonly used assumptions for high-dimensional set up is also briefly discussed.

Place, publisher, year, edition, pages
Linköping, 2011. , 28 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2011:13
Keyword [en]
covariance testing; high dimensional data; sphericity
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-70062Local ID: LiTH-MAT-R--2011/13--SEOAI: oai:DiVA.org:liu-70062DiVA: diva2:435111
Available from: 2011-08-17 Created: 2011-08-17 Last updated: 2014-09-29

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Ahmad, M. RaufOhlson, Martin

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