Statistical Inference for Uniform Stochastic Ordering in Several Populations

摘要: Stochastic ordering between probability distributions is a widely studied concept. It arises in numerous settings and has useful applications. Since it often easy to make value judgments when such orderings exist, desirable recognize their occurrence model distributional structure under orderings. Unfortunately, the necessary theory for statistical inference procedures not been developed many problems involving stochastic this development seems be difficult task. We show paper that stronger notion of uniform (which equivalent failure rate continuous distributions) quite tractable matters inference. In particular, we consider nonparametric maximum likelihood estimation $k$-population restrictions. derive closed-form estimates even with right-censored data by reparameterization which reduces problem well-known isotonic regression problem. also asymptotic distribution ratio statistic testing equality $k$ populations against restriction. This chi-bar-square type as discussed Robertson, Wright Dykstra. These results are obtained appealing elegant from empirical process showing proposed test asymptotically free. Recurrence formulas derived weights particular cases. The illustrated an example survival times carcinoma oropharynx.