Estimating \(p\)-values for Mardia's coefficients of multivariate skewness and kurtosis
This paper deals with a test of multivariate normality based on Mardia's estimates of multivariate skewness \(z_1\) and kurtosis \(z_2\). While the properly normalized statistics \(z_1\) and \(z_2\) asymptotically have a \(\chi^2\) and normal distribution, respectively, Mardia's test does not perform well in small sample cases. A Monte-Carlo method for estimation of the critical p-values for Mardia's \(z_1\) and \(z_2\) statistics is proposed and illustrated.
scientific article; zbMATH DE number 1865443