Order restricted inference for hypotheses concerning qualitative dispersion

We discuss likelihood-based order restricted inference for hypotheses concerning the qualitative dispersion associated with a probability vector; levels of dispersion are compared using the concept of Schur majorization. In particular, we show how to compute the maximum likelihood estimates of a probability vector under certain equality and inequality constraints on the dispersions, and show that the corresponding estimators are consistent. Asymptotic null distributions of the likelihood ratio statistics are also derived. Two data sets are analyzed using the methods developed in this paper.