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Tests of Covariance...
Tests of Covariance Matrices for High Dimensional Multivariate Data Under Non Normality
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- Ahmad, M. Rauf (author)
- Swedish University of Agricultural Sciences,Sveriges lantbruksuniversitet,Uppsala universitet,Statistiska institutionen,Institutionen för energi och teknik,Department of Energy and Technology,Uppsala University,Uppsala University, Sweden; Swedish University of Agriculture Science, Sweden
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- Von Rosen, Dietrich (author)
- Linköpings universitet,Swedish University of Agricultural Sciences,Sveriges lantbruksuniversitet,Institutionen för energi och teknik,Department of Energy and Technology,Linköping University,Matematisk statistik,Tekniska högskolan,Swedish University of Agriculture Science, Sweden
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(creator_code:org_t)
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- 2013-06-20
- 2015
- English.
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In: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 44:7, s. 1387-1398
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Abstract
Subject headings
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- Ahmad et al. (in press) presented test statistics for sphericity and identity of the covariance matrix of a multivariate normal distribution when the dimension, p, exceeds the sample size, n. In this note, we show that their statistics are robust to normality assumption, when normality is replaced with certain mild assumptions on the traces of the covariance matrix. Under such assumptions, the test statistics are shown to follow the same asymptotic normal distribution as under normality for large p, also whenp >> n. The asymptotic normality is proved using the theory of U-statistics, and is based on very general conditions, particularly avoiding any relationship between n and p.
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Non normality
- High dimensionality
- Sphericity
Publication and Content Type
- ref (subject category)
- art (subject category)
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