The null distribution of multivariate kurtosis

The paper introduces a x²-approximation to multivariate kurtosis b_2,punder normality. It requires calculating the third moment of b_2,pwhich is obtained. We compare the approximation with simulated percentage points and the normal approximation, and find it to be adequate for p=l and 2. For p=3, the simple average of this estimate and the normal approximation is found to be generally superior to either approximation on its own. For p=4, the normal approximation is best for non-extreme values of ∝