Omnibus Tests for Multivariate Normality of Observations and Residuals

This paper provides omnibus tests for multivariate normality of both observations and residuals. They are derived by considering as the alternatives to the multivariate normal a class of maximum-entropy distributions studied elsewhere by the author. The tests, being Lagrange multiplier statistics, have optimum local asymptotic power among those alternatives. Furthermore, they coincide in the univariate case with the popular Jarque-Bera test for normality. They also include as special cases several multivariate tests available in the literature. Finally, the paper also suggests simple adjustments that can significantly improve the power of the tests in the case of small and medium size samples, even for the univariate case.