Statistical inference for the two-sample problem under likelihood ratio ordering, with application to the ROC curve estimation

Likelihood ratio ordering has been identified as a reasonable assumption in the two-sample problem in many practical scenarios. With this assumption, statisticians have proposed various methods in the estimation of the distributions of subpopulations, which consequently benefit the downstream inferences, such as the ROC curve and the associated summary statistic estimation. In this paper, under the likelihood ratio ordering assumption, we first propose a Bernstein polynomial method to model the distributions of both samples; we then estimate the distributions by the maximum empirical likelihood principle. The ROC curve estimate and the associated summary statistics are obtained subsequently. We compare the performance of our method with existing methods by extensive simulation studies. The application of our method is illustrated by a real-data example.