Tests of Covariance Matrices for High Dimensional Multivariate Data Under Non Normality

Ahmad, M. RaufSwedish 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 (author)

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.

Von Rosen, DietrichLinköpings 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(Swepub:liu)dievo64 (author)
Uppsala universitetStatistiska institutionen (creator_code:org_t)
Sveriges lantbruksuniversitet

In:Communications in Statistics - Theory and Methods: Informa UK Limited44:7, s. 1387-13980361-09261532-415X

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NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Probability Theo ...

By the university: Uppsala University; Swedish University of Agricultural Sciences; Linköping University

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