On the asymptotic distribution of T²-type statistic with two-step monotone missing data

ABSTRACT

In this article, we consider the asymptotic distribution of Hotelling’s T²-type test statistic when a two-step monotone missing data set is drawn from a multivariate normal population under a large-sample asymptotic framework. In particular, asymptotic expansions for the distribution and upper percentiles are derived using a perturbation method up to the terms of order n⁻¹, where n = N – 2 and N denotes the total sample size. Furthermore, making use of Fujikoshi’s transformations, we also have Bartlett-type corrections of the test statistic considered in this article. Finally, we investigate the performance of the proposed approximation to the upper percentiles and Bartlett-type correction for the test statistic by conducting Monte Carlo simulations for some selected parameters.

KEYWORDS:

• asymptotic expansion
• Bartlett correction
• chi-squared approximation
• Monte Carlo simulation
• stochastic expansion
• two-step monotone missing data

AMS SUBJECT CLASSIFICATION:

• 62H15
• 62H10

Acknowledgments

The authors extend their sincere gratitude to the editor, who gave invaluable comments and suggestions that have enhanced this article.

Additional information

Funding

The research of the last two authors was supported in part by a Grant-in-Aid for Young Scientists (B) (16K17642) and Grant-in-Aid for Scientific Research (C) (17K00058) from the Japan Society for the Promotion of Science.