Some empirical distribution function tests for multivariate normality

Abstract

Abstract This paper presents finite sample percentage points of the Anderson-Darling (AD) statistic for testing the composite hypothesis of Gaussianity (normality) for dimensionality 1≦p≦5 when the parameters are estimated from data. This paper also presents asymptotic percentage points for both the Anderson-Darling and the Cramervon Mises(CM) statistics for testing the composite hypothesis of Gaussianity for dimensionality 1≦p≦25 when the parameters are estimated from data. The AD test is developed from the fact that the quadratic form of the Gaussian density is distributed as chi-squared on p degrees of freedom. A small power study contrasts the finite sample performance of the AD and CM statistics. Several examples are discussed in the context of chi-squared probability plotting. †Research sponsored in part by the U.S. Army Research Office under contract DAA G29-81-K-0110 and under contract CL766634 with IBM ‡Research sponsored in part by contract CL766634 with IBM †Research sponsored in part by the U.S. Army Research Office under contract DAA G29-81-K-0110 and under contract CL766634 with IBM ‡Research sponsored in part by contract CL766634 with IBM Notes †Research sponsored in part by the U.S. Army Research Office under contract DAA G29-81-K-0110 and under contract CL766634 with IBM ‡Research sponsored in part by contract CL766634 with IBM