A MULTIVARIATE EXTENSION OF SHAPIRO-WILK'S TEST AND POWER INVESTIGATION FOR MIXED ALTERNATIVESJournal: International Journal of Applied Mathematics & Statistical Sciences (IJAMSS) (Vol.5, No. 1)
Publication Date: 2016-01-31
Authors : R. SAKTHIVEL; MARTIN L. WILLIAM;
Page : 49-62
Keywords : Testing Multivariate Normality; Mixtures of Distributions; Monte Carlo Simulation;
It is well known that even though many procedures are available for testing univariate normality, the procedure developed by Shapiro and Wilk (1965) is a very effective and powerful test to detect a variety of departures from normality. A generalization of the Shapiro-Wilk procedure to test for multivariate normality has been given recently by Alva and Estrada (2009). The present paper considers a different approach to extend the Shapiro-Wilk procedure for testing multivariate normality. An extensive simulation has been carried out to generate the critical values of the proposed statistic for dimensions 2 and 5. Power comparison of the new approach to the one given by Alva and Estrada (2009) is presented for a choice of mixed alternatives. The software for this work is developed in R Language.
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