Tests for Equality of Mean Vectors and Simultaneous Confidence Intervals with Two-Step or Three-Step Monotone Missing Data Patterns

SYNOPTIC ABSTRACT

In this article, we consider the problem of testing the equality of two mean vectors when the data have a three-step monotone pattern of missing observations. We propose an approximate upper percentile of the Hotelling’s T²-type statistic in which each dataset has a three-step monotone missing data pattern and the population covariance matrices are equal. Further, we obtain the Hotelling’s T²-type statistics and their approximate upper percentiles in the case of data with unequal two-step monotone missing data patterns. We also consider multivariate multiple comparisons for mean vectors with three-step monotone missing data. Approximate simultaneous confidence intervals for pairwise comparisons among mean vectors and comparisons with a control are obtained using Bonferroni’s approximate upper percentiles of the T²_{max · p} and T²_{max · c} statistics, respectively. Finally, the accuracy of the approximations is investigated via Monte Carlo simulation.

Key Words and Phrases::

• comparisons with a control
• Hotelling’s T²-type statistic
• maximum likelihood estimator
• pairwise comparisons
• two-sample problem.