LBI tests for multivariate normality in exponential power distributions

Abstract

In the class of multivariate exponential power distributions, we derive LBI (locally best invariant) tests for normality in the two cases: (i) mean vector μ is known and (ii) μ is unknown. In the case (i), the null and nonnull asymptotic distributions of the test statistic are derived. In the case (ii) the asymptotic properties of the LBI test remain open because of a technical difficulty. However, the null distribution of a modified test is derived. A Monte Carlo study on the percentage points of the tests is made.