On Boundary Correction in Kernel Estimation of ROC Curves

Abstract

The Receiver Operating Characteristic (ROC) curve is a statistical tool for evaluating the accuracy of diagnostics tests. The empirical ROC curve (which is a step function) is the most commonly used non-parametric estimator for the ROC curve. On the other hand, kernel smoothing methods have been used to obtain smooth ROC curves. The preceding process is based on kernel estimates of the distribution functions. It has been observed that kernel distribution estimators are not consistent when estimating a distribution function near the boundary of its support. This problem is due to “boundary effects” that occur in nonparametric functional estimation. To avoid these difficulties, we propose a generalized reflection method of boundary correction in the estimation problem of ROC curves. The proposed method generates a class of boundary corrected estimators.