Semi‐parametric maximum likelihood estimates for ROC curves of continuous‐scale tests

In this paper, we propose a new semi‐parametric maximum likelihood (ML) estimate of a receiver operating characteristic (ROC) curve that satisfies the property of invariance of the ROC curve and is easy to compute. We show that our new estimator is $$ \sqrt {n} $$ ‐consistent and has an asymptotically normal distribution. Our extensive simulation studies show that the proposed method is efficient and robust. Finally, we illustrate the application of the proposed estimator in a real data set. Copyright © 2008 John Wiley & Sons, Ltd.