On disparity based goodness-of-fit tests for multinomial models

A general class of goodness-of-fit tests called disparity tests containing the family of power weighted divergence statistics as a subclass is considered. Under the simple and composite null hypotheses the asymptotic distribution of disparity tests is shown to be chi-square. It is also shown that the blended weight Hellinger distance subfamily, like the power weighted divergence subfamily, has a member that gives an excellent compromise between the Pearson's chi-square and the log likelihood ratio tests.