Inference for Multinomial Parameters and Odds Ratios under Order Restrictions

This paper presents strategies for the estimation and testing of binomial and multinomial parameters as well as odds ratios under order restrictions. Estimates of binomial and multinomial parameters under certain order restrictions are obtained and subsequently used in the estimation of the odds ratios. Also, estimates that make use of the marginal frequencies are obtained and studied. The estimated bias and mean square error of the estimates are given. Test procedures are developed based on these estimates and their distributions given. Appropriate comparisons of the estimates as well as the developed test procedures are given for sparse to moderate samples. Furthermore, the results presented are extended to cover alternative reparametrization using appropriate terminology for failure time data