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http://dx.doi.org/10.5351/CSAM.2015.22.4.361

Tests Based on Skewness and Kurtosis for Multivariate Normality  

Kim, Namhyun (Department of Science, Hongik University)
Publication Information
Communications for Statistical Applications and Methods / v.22, no.4, 2015 , pp. 361-375 More about this Journal
Abstract
A measure of skewness and kurtosis is proposed to test multivariate normality. It is based on an empirical standardization using the scaled residuals of the observations. First, we consider the statistics that take the skewness or the kurtosis for each coordinate of the scaled residuals. The null distributions of the statistics converge very slowly to the asymptotic distributions; therefore, we apply a transformation of the skewness or the kurtosis to univariate normality for each coordinate. Size and power are investigated through simulation; consequently, the null distributions of the statistics from the transformed ones are quite well approximated to asymptotic distributions. A simulation study also shows that the combined statistics of skewness and kurtosis have moderate sensitivity of all alternatives under study, and they might be candidates for an omnibus test.
Keywords
Goodness of fit tests; multivariate normality; skewness; kurtosis; scaled residuals; empirical standardization; power comparison;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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