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Tests of Covariance Matrices for High Dimensional Multivariate Data Under Non Normality
Uppsala University, Sweden; Swedish University of Agriculture Science, Sweden.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology. Swedish University of Agriculture Science, Sweden.
2015 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 44, no 7, 1387-1398 p.Article in journal (Refereed) Published
Abstract [en]

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 greater thangreater than 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.

Place, publisher, year, edition, pages
Taylor and Francis , 2015. Vol. 44, no 7, 1387-1398 p.
Keyword [en]
Non normality; High dimensionality; Sphericity
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-117394DOI: 10.1080/03610926.2013.770533ISI: 000352005700005OAI: oai:DiVA.org:liu-117394DiVA: diva2:807754
Available from: 2015-04-24 Created: 2015-04-24 Last updated: 2015-04-24

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