A simple but highly competitive method of testing the assumption of multivariate normality

Oftentimes, a multivariate data set, which is made up of n independent data points in d variables, is assumed to have been obtained as a random sample from a multivariate distribution. For a good number of reasons, the most important of all the existing multivariate distributions, which is also mostly used in real life, is the multivariate normal distribution. A good number of test procedures to ascertain if a data set of this kind is obtained from the multivariate normal distribution exist in the literature. They however vary in simplicity/complexity as well as in efficiency. The efficiency of the goodness-of-fit test of this kind, known as the power of the test, is the ability of the test to take a right decision of rejecting the hypothesis of multivariate normality (MVN) of the data set when it is actually right to be rejected. My research area is to combine these two important properties of simplicity of tests for MVN as well as highly competitiveness of the tests in terms of power. This will help users of statistics, especially those who do not have very strong background in statistical theory to apply the test with comparative ease yet loosing nothing in terms of the correctness of their decision. The paper we developed here is founded on this philosophy. It is more powerful than most tests for MVN found in the literature. It is therefore hoped that applied statisticians would find it very interesting.