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 : (k) against H1 : at least two (i) s 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.