Some empirical distribution function tests for multivariate normality

摘要

This paper presents finite sample percentage points of the Anderson-Darling (AD) statistic for testing the composite hypothesis of Gaussianity (normality) for dimensionality 1#x2266;p#x2266;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#x2266;p#x2266;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 onpdegrees 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.