ON A NEW AFFINE INVARIANT AND CONSISTENT TEST FOR
MULTIVARIATE NORMALITY
Abstract: We propose a new test for multivariate normality based on the empirical
characteristic function. We show that the test is affine invariant and consistent against every
non-normal alternative. The test considered in this paper is also able to detect contiguous
alternatives that converge to the normal distribution at the rate The results of an
extensive Monte Carlo study show that the test has power comparable with one of the best
existing procedures.
2000 AMS Mathematics Subject Classification: 62G10 (62H15).
Key words and phrases: Test for multivariate normality, empirical characteristic
function, goodness-of-fit-test.