Minimum distance estimation of the Lehmann receiver operating characteristic curve

Abstract

A receiver operating characteristic (ROC) curve based on the Lehmann family of distributions has a very simple form and is an important alternative to the popular binormal ROC curve. In this paper, we propose to use the minimum distance method to estimate a one-dimensional parameter of this curve. We prove the consistency and asymptotic normality of estimators obtained by applying various measures of discrepancy. In a simulation study, we compare the accuracy of the estimators proposed with the accuracy of a known estimator based on a partial likelihood method and an estimator based on the estimation of the area under the curve. We also provide an illustrative example of an application to real data.