Remarks on the Test of Multivariate Normality by Union Intersection Principle

• Activity Number: 308
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Chun-Chao Wang and Yi-Ting Hwang*+
• Companies: National Taipei University and National Taipei University
• Keywords: Multivariate normality ; Shapiro-Wilk statistic ; Union intersection principle ; Monte Carlo simulation ; Projection Pursuit

Abstract

Among various multivariate normality tests, the one that employ Roy's union-intersection principle (Roy, 1953) is shown to be empirically competitive. These tests convert a hypothesis of multivariate normality into an infinite number of hypotheses of univariate normality and result in solving a constraint multivariate optimization problem. Due to the difficulty in solving the multivariate optimization problem, various approximations are proposed to substitute the global one. However, this paper discovers that the nearly global solution contrarily results in unsatisfactory performance in power through the Monte Carlo simulations. Thus, instead of searching for a true optimal solution, the qth percentile of the objective function values is suggested to be a suitable substitute in an empirical sense. A Monte Carlo study shows the proposed method is superior to two highly recommended tests.