Testing multivariate normality by simulation

Abstract

The purpose of this paper is to propose a method of testing multivariate normality which guarantees the asymptotic size of the test. The basic idea is simulation of the actual percentage points of the distribution of a test statistic over a grid in a confidence region. Other tools which are called into service include non-parametric density estimation, likelihood ratio statistics, and spline interpolation. The procedure is compared with three well-known tests in a small simulation experiment.