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A note on mean testing for high dimensional multivariate data under non-normality
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- Ahmad, M. Rauf (author)
- Sveriges lantbruksuniversitet,Uppsala universitet,Statistiska institutionen,Swedish University of Agricultural Sciences, Uppsala, Sweden and Department of Statistics, Uppsala University, Sweden,Institutionen för energi och teknik,Department of Energy and Technology
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- von Rosen, Dietrich (author)
- Swedish University of Agricultural Sciences,Sveriges lantbruksuniversitet,Linköpings universitet,Matematisk statistik,Tekniska högskolan,Institutionen för energi och teknik,Department of Energy and Technology
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- Singull, Martin, 1977- (author)
- Linköpings universitet,Matematisk statistik,Tekniska högskolan
- (creator_code:org_t)
- 2012-08-02
- 2013
- English.
- In: Statistica Neerlandica. - : Wiley. - 0039-0402 .- 1467-9574. ; 67:1, s. 81-99
- Journal article (peer-reviewed)
Abstract
Subject headings
Close
- 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?8, 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Keyword
- non-normality;high dimensionality;Box's approximation
Publication and Content Type
- ref (subject category)
- art (subject category)
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