A Test for Mean Vector and Simultaneous Confidence Intervals with Three-Step Monotone Missing Data

SYNOPTIC ABSTRACT

In this article, we consider the problem of testing for mean vector and simultaneous confidence intervals when the data have a three-step monotone pattern that is missing observations. The maximum likelihood estimators of the mean vector and the covariance matrix with a three-step monotone missing data pattern are presented based on the derivation of Jinadasa and Tracy (1992). We propose an approximate upper percentile of Hotelling’s T²-type statistic to test the mean vector. Further, we obtain the approximate simultaneous confidence intervals for any and all linear compounds of the mean and the testing equality of mean components. Finally, the accuracy of the approximation is investigated by Monte Carlo simulation, and a numerical example is given to illustrate the method.

Key Words and Phrases::

• T²-type statistic
• maximum likelihood estimator
• three-step monotone missing data.