Tests for mean vectors with two-step monotone missing data for the k-sample problem

We continue our recent work on the problem of testing the equality of two normal mean vectors when the data have two-step monotone pattern missing observations. This paper extends the two-sample problem in our previous paper to the k-sample problem. Under the assumption that the population covariance matrices are equal, we obtain the likelihood ratio test statistic for testing the hypothesis H0 : μ (1) = μ = · · · = μ against H1 : at least two μs are unequal. Then, we provide Hotelling’s T 2 type statistic for testing any two mean vectors and propose the approximate upper percentile of this statistic. The accuracy of the approximation is investigated by Monte Carlo simulation. AMS 2010 Mathematics Subject Classification. 62H10, 62E20, 62H15.