Nonparametric Estimation Of The ROC Curve Based On The Bernstein Polynomial

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 and it is proved that the estimator has the Chung Smirnov property.We establish the pointwise asymptotic normality of the Bernstein ROC estimator.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.In addition,the expression of the optimal parameter is given and the assumptions given in the theorem are weakened.Furthermore,the weak convergence of the Bernstein ROC process is established and it is compared to that of the empirical ROC process.Simulation studies are conducted to compare our proposed estimator with other popular nonparametric ROC estimators.The quality of the estimators is evaluated globally by both MISE and MSN and we discuss the advantages and disadvantages of each estimator in different cases.Finally,the proposed estimator and its competitors are illustrated by application to a real data set which comes from a clinical study and the area under curve(AUC)is calculated.