Testing Equality of Two Mean Vectors with Two-Step Monotone Missing Data

SYNOPTIC ABSTRACT

We consider the problem of testing for two normal mean vectors when the data have two-step monotone pattern missing observations. Under the assumption that the population covariance matrices are equal, we obtain two test statistics for this problem: a generalized Hotelling's T² test statistic and the likelihood ratio test statistic. We propose the approximate upper percentiles of these statistics. The accuracy of the approximation is investigated by Monte Carlo simulation. The proposed method is illustrated using an example.

Key words and phrases:

• Hotelling's T² type statistic
• Likelihood ratio test
• Two sample problem
• Maximum likelihood estimator
• Simultaneous confidence interval
• Two-step monotone missing data