On the Asymptotic Normality of Test Statistics Using Song’s Kurtosis
In this article, we consider the multivariate normality test based on the sample measure of multivariate kurtosis defined by Song (2001). We calculate moments of Song’s kurtosis when covariance matrix Σ is known and unknown. In addition, we derive expectations and variances of the multivariate sample kurtosis under normality and propose three standardized test statistics using these expectations and variances. When Σ is known, we also propose a test statistic whose approximate accuracy for multivariate normal distribution is improved rather than the standardized statistics by normalizing transformation. In order to evaluate accuracy of proposed test statistics, the numerical results by Monte Carlo simulation for some selected values of parameters are presented.
KeywordsMultivariate kurtosis multivariate normality test normalizing transformation
AMS Subject Classifications62D05 62H10
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- Enomoto, R., N. Okamoto, and T. Seo. 2012. On the distribution of test statistic using Song’s kurtosis. Technical report No.12-02, Statistical Research Group, Hiroshima University, Hiroshima, Japan.Google Scholar