On the New Algorithm of Testing and Comparing Size Corrected Powers for Testing Multivariate Normality

Abstract

Parametric models are mainly based on univariate or multivariate normality assumptions. Uniformly most powerful (UMP) test is not available to test multivariate normality. In such a situation, optimal test can be used. But, a very few literature is available on the size corrected power comparison of different multivariate normality tests. In this paper, we propose an algorithm to compare the size corrected powers for testing univariate or multivariate normality. The algorithm can be applied to any existing univariate and multivariate tests, which is the most attractive feature of the proposed new algorithm. We also propose a Cholesky decomposition of the variance-covariance matrix based test, which is simpler than the existing test. Our Monte Carlo simulation study indicates that our proposed and existing tests perform equally in terms of power properties.

Keywords— Cholesky decomposition, UMP test, Optimal test, Monte Carlo.