Disparity based goodness-of-fit tests for and against order restrictions for multinomial models

We consider disparity based test statistics to test the equality of a multinormal probability vector to a given probability vector against an isotonic/antitonic order restriction. The problem of testing the isotonic restriction as a null hypothesis against unrestricted alternatives is also considered. In both cases the asymptotic distributions of these test statistics are found to be of the chi-bar squared type similar to the popular likelihood ratio test statistics for these cases. However our numerical studies demonstrate that depending on the situation, several of the disparity test statistics are more powerful than the latter.