Tests for mean vector with two-step monotone missing data

Abstract

We consider the problem of testing for multivariate mean vector when the data have two-step monotone pattern missing observations. We obtain two test statistics for this problem: a test statistic similar to Hotelling’s $T^2$ 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. A test statistic for the components of mean vector is outlined. Approximate simultaneous confidence intervals are obtained and the proposed method is illustrated using an example.