Multivariate normality test based on kurtosis with two-step monotone missing data

Abstract

This paper deals with a sample measure of multivariate kurtosis, which is used as a test statistic in multivariate normality testing problems. We define a new multivariate sample kurtosis measure to provide a multivariate normality test for data with a two-step monotone missing structure. Furthermore, we derive its expectation and variance using a perturbation method. To evaluate the accuracy of a normal approximation, we conducted a Monte Carlo simulation for certain parameters. Finally, we present a numerical example to illustrate the proposed procedure.