A MULTIVARIATE EXTENSION OF SHAPIRO-WILK'S TEST AND POWER INVESTIGATION FOR MIXED ALTERNATIVES

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.