A generalized Shapiro-Wilk W statistic for testing high-dimensional normality

Jiajuan Liang*, Man Lai TANG, Ping Shing Chan

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

32 Citations (Scopus)


Shapiro and Wilk's [Shapiro, S.S., Wilk, M.B., 1965. An analysis of variance test for normality (complete samples). Biometrika 52, 591-611] W-statistic was found to have competitive power performance in testing univariate normality. Generalizations of the W-statistic to the multivariate case have been proposed by many researchers. In this paper, we propose a family of generalized W-statistics for testing high-dimensional normality by using the theory of spherical distributions. The proposed statistics apply to the case that the sample size is smaller than the dimension. Monte Carlo studies demonstrate feasible performance of the proposed tests in controlling type I error rates and power against some non-normal data. It is concluded that the proposed statistics are superior to existing generalizedW-statistics and show competitive benefits in testing high-dimensional normality with small sample size.

Original languageEnglish
Pages (from-to)3883-3891
Number of pages9
JournalComputational Statistics and Data Analysis
Issue number11
Publication statusPublished - 1 Sept 2009

Scopus Subject Areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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