INFERENCE FOR LIKELIHOOD RATIO ORDERING IN THE 2-SAMPLE PROBLEM

We obtain the maximum likelihood estimators of two multinomial probabi lity vectors under the constraint that they are likelihood ratio order ed. We extend this estimation approach to the case of two univariate d istributions and show strong consistency of the estimators. We also de rive and study the asymptotic distribution of the likelihood ratio sta tistic for testing the equality of two discrete probability distributi ons against the alternative that one distribution is greater than the other in the likelihood ratio ordering sense. Finally, we examine a da ta set pertaining to average daily insulin dose from the Boston Collab orative Drug Surveillance Program and compare our testing procedure to testing procedures for other stochastic orderings.