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

Eri Kurita and Takashi Seo

International Journal of Statistics and Probability, 2025, vol. 13, issue 3, 1

Abstract: 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.

Date: 2025
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