Minimum-norm estimation for binormal receiver operating characteristic (ROC) curves

The receiver operating characteristic (ROC) curve is often used to assess the usefulness of a diagnostic test. We present a new method to estimate the parameters of a popular semi-parametric ROC model, called the binormal model. Our method is based on minimization of the functional distance between two estimators of an unknown transformation postulated by the model, and has a simple, closed-form solution. We study the asymptotics of our estimators, show via simulation that they compare favorably with existing estimators, and illustrate how covariates may be incorporated into the norm minimization framework.