Tests for Multivariate Kurtosis With Two- and Three-step Monotone Missing Data

In this paper, we consider the test statistic for multivariate kurtosis and its percentiles of the null distribution to test for multivariate normality with monotone missing data. In particular, we formulate a test statistic for which the normal approximation in the case of two-step monotone missing data is given by the expectation and variance approximated by linear approximation. Furthermore, we extend this statistic to the case of three-step monotone missing data. Specifically, we define multivariate sample kurtosis for three-step monotone missing data, and formulate a new test statistic that uses information approximated by linear interpolation. Finally, we investigate the accuracy and behavior of the normal approximation by a Monte Carlo simulation.