Two-sample inference for normal mean vectors based on monotone missing data

Inferential procedures for the difference between two multivariate normal mean vectors based on incomplete data matrices with different monotone patterns are developed. Assuming that the population covariance matrices are equal, a pivotal quantity, similar to the Hotelling T² statistic, is proposed, and its approximate distribution is derived. Hypothesis testing and confidence estimation of the difference between the mean vectors based on the approximate distribution are outlined. The validity of the approximation is investigated using Monte Carlo simulation. Monte Carlo studies indicate that the approximate method is very satisfactory even for small samples. A multiple comparison procedure is outlined and the proposed methods are illustrated using an example.