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A note on mean testing for high dimensional multivariate data under non-normality
Swedish University of Agricultural Sciences, Uppsala, Sweden and Department of Statistics, Uppsala University, Sweden.
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
2013 (English)In: Statistica neerlandica (Print), ISSN 0039-0402, E-ISSN 1467-9574, Vol. 67, no 1, 81-99 p.Article in journal (Refereed) Published
Abstract [en]

A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n,p→∞, and under mild assumptions, but without assuming any relationship between n and p, the statistic is shown to asymptotically follow a chi-square distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of the well-known Box's approximation, under high-dimensional set up. Using a classical limit theorem, the approximation is further extended to an asymptotic normal limit under the same high dimensional set up. The simulation results, generated under different parameter settings, are used to show the accuracy of the approximation for moderate n and large p.

Place, publisher, year, edition, pages
2013. Vol. 67, no 1, 81-99 p.
Keyword [en]
non-normality;high dimensionality;Box's approximation
National Category
Probability Theory and Statistics
URN: urn:nbn:se:liu:diva-87379DOI: 10.1111/j.1467-9574.2012.00533.xISI: 000313270000005OAI: diva2:589044
Available from: 2013-04-03 Created: 2013-01-16 Last updated: 2014-09-29Bibliographically approved

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