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A two-sample test statistic for high-dimensional multivariate data under non-normality
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
2011 (English)Report (Other academic)
Abstract [en]

Ahmad, Ohlson, and von Rosen (2011a) present asymptotic distribution of a one-sample test statistic under non-normality, when the data are high dimensional, i.e., when the dimension of the vector, p, may exceed the sample size, n. This paper extends the case to a two-sample statistic to test the difference of mean vectors of two independent multivariate distributions, again under high-dimensional set up. Using the asymptotic theory of U-statistics, and under mild assumptions on the traces of the unknown covariance matrices, the statistic is shown to follow an approximate normal distribution when n and p are large. However, no relationship between n and p is assumed. An extension to the paired case is given, which, being essentially a one-sample statistic, supplements the asymptotic results obtained in Ahmad, Ohlson, and von Rosen (2011a).

Place, publisher, year, edition, pages
Linköping, 2011. , 17 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2011:12
Keyword [en]
two-sample test, high-dimensionality, U-statistics
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:liu:diva-70060Local ID: LiTH-MAT-R-2011-12OAI: oai:DiVA.org:liu-70060DiVA: diva2:435096
Available from: 2011-08-17 Created: 2011-08-17 Last updated: 2013-11-26

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Ahmad, M. Rauf

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