LBI TESTS FOR MULTIVARIATE NORMALITY IN EXPONENTIAL POWER DISTRIBUTIONS

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. © 1991.