Nonparametric estimation of the ROC curve based on the Bernstein polynomial

Abstract

The receiver operating characteristic (ROC) curve is a graphical representation of the relationship between false positive and true positive rates. It is a widely used statistical tool for describing the accuracy of a diagnostic test. In this paper we adopt Bernstein polynomials to construct the ROC curve estimator. The consistency rate of this estimator is studied. We also obtain explicit expressions for the asymptotic bias and variance and show the improvement of the asymptotic mean squared error compared to that of the classical empirical ROC estimator. Furthermore, the weak convergence of the Bernstein ROC process is established. Simulation studies are conducted to compare our proposed estimator with other popular nonparametric ROC estimators. Finally, the proposed method is illustrated by application to a real data set.