Title: A new class of tests for multinormality based on the moment generating function
Authors: Norbert Henze - Karlsruhe institute of Technology (Germany)
Jaco Visagie - University of Pretoria, South Africa (South Africa) [presenting]
Abstract: It is often of interest to determine whether or not observed data are realised from a multivariate normal distribution. We propose a new class of affine invariant tests for multinormality based on the empirical moment generating function. The proposed test statistic contains a tuning parameter. We show that, after suitable scaling, the test statistic approaches a linear combination of two well-known measures of multivariate skewness for fixed sample sizes as the tuning parameter tends to infinity. We also derive the limit distribution of the test statistic for large samples under the null hypothesis of multinormality. A Monte Carlo power study is conducted in order to compare the finite sample performance of the proposed test to various existing tests.