Mardia's Multivariate Kurtosis with Missing Data

Abstract

Mardia's measure of multivariate kurtosis has been implemented in many statistical packages commonly used by social scientists. It provides important information on whether a commonly used multivariate procedure is appropriate for inference. Many statistical packages also have options for missing data. However, there is no procedure for applying Mardia's kurtosis to a data set with missing values. In this article Mardia's kurtosis is extended to a dataset with missing values. Based on the complete data counterpart, the behavior of a standardized version of the extended sample kurtosis can be described by the standard normal distribution. Analytical and Monte-Carlo studies imply that the proposed distribution description is as good as its complete data counterpart when missing variables are either missing completely at random or missing at random when observed marginals do not sit in a cluster with a restricted range. Application of this procedure is illustrated with a real data set.