Receiver Operating Characteristic Curve and Equal Error Rate

Abstract

This chapters provides methodology for statistical inference concerning receiver operating characteristic (ROCs) curves and equal error rates (EER’). We begin with an introduction to the ROC with special focus on a polar coordinates representation of the ROC. We then propose a new bootstrap methodology for estimation of the variability in a sample ROC. Next we discuss our methodology for making curvewise confidence regions for the ROC. This methodology forms the basis for our approach to inference for the rest of the chapter. Having presented our methodology for a single ROC, we move to methods for comparing two ROC’s. We do this both for the case when the ROC’s are collected independently as well as when the matching scores are collected in a paired manner. Comparisons of three or more ROC’s whether paired or independent is the last topic on ROC’s in this chapter. Our focus then moves to statistical methods for equal error rates (EER’s). Our organization for the part of this chapter on EER’s is similar to our structure for ROC inference. We start with estimation for a single EER. This is followed by methodology for comparing two EER’s and then comparing three or more EER’s. Both sections have descriptions of comparisons for independent and paired data collection. This chapter ends with a further discussion of some of these topics.