Test for multivariate normality based on new characterization

Abstract

The standard multivariate normal distribution is characterized through a certain linear combination being constant on a unit n-sphere. Based on this characterization, some normality tests are constructed. The main emphasis is on the null hypothesis of multivariate normal distribution with diagonal covariance matrix. We explore the asymptotic properties and perform a simulation study. We also consider the case of a general covariance matrix. The tests perform well in comparison to some popular powerful competitors. Potential applications are also discussed.