Tests for Normal Mean Vectors with Monotone Incomplete Data

SYNOPTIC ABSTRACT

In this article, we consider the distributions of the Hotelling’s T²-type test statistics for mean vectors when each dataset has a monotone missing data pattern. We give the approximate upper percentiles of the simplified Hotelling’s T²-type statistics in the case of data with k-step monotone missing data patterns. We also consider multivariate multiple comparisons for mean vectors with k-step monotone missing data. Approximate simultaneous confidence intervals for pairwise comparisons among mean vectors and comparisons with a control are obtained using Bonferroni’s approximation procedure. Finally, the accuracy and asymptotic behavior of the approximations are investigated by Monte Carlo simulation.

KEY WORDS AND PHRASES:

• Hotelling’s T²-type statistic
• maximum likelihood estimator
• multiple comparisons
• one-sample problem
• two-sample problem

Acknowledgments

The authors would like to thank two referees for their helpful comments and suggestions. The first and second authors’ research was partly supported by a Grant-in-Aid for JSPS Fellows (15J00414) and a Grant-in-Aid for Scientific Research (C) (26330050), respectively.