Testing for and against a set of inequality constraints: The k-sample case

In this paper we aim to generalize the existing results and provide a test for testing for and against a set of inequality constraints placed upon any k ( k ⩾ 1 ) vectors of parameters corresponding to k populations. The approach we take is the likelihood ratio approach. We show that the limiting distributions of the likelihood ratio test are of chi-bar square type and provide the expression of the weighting values. Examples are discussed to illustrate the theoretical results.