More efficient estimators of the area under the receiver operating characteristic curve in paired ranked set sampling

Abstract

Receiver operating characteristic is a beneficial technique for evaluating the performance of a binary classification. The area under the curve of the receiver operating characteristic is an effective index of the accuracy of the classification process. While nonparametric point estimation has been well-studied under the ranked set sampling, it has received little attention under ranked set sampling variations. In order to set out to fill this gap, this article deals with the problem of estimating the area under the curve of the receiver operating characteristic based on paired ranked set sampling. New estimators of the area under the curve of the receiver operating characteristic based on paired ranked set sampling are proposed. Using the information supported by the concomitant variable, the additional area under the curve of the receiver operating characteristic estimators based on ranked set sampling as well as paired ranked set sampling are also introduced. It is shown either theoretically or numerically that the proposed estimators are consistent under the perfectness situation. It emerges that the concomitant-based estimators are shown to be superior to their competitors provided that the perfect assumption is not sharply violated. In contrast, kernel-based estimators are significantly superior relative to their rivals regardless of the quality of ranking. Finally, the application of the proposed procedures is also demonstrated by using empirical datasets in the context of medicine.