Smoothing Kernel Estimator for the ROC Curve-Simulation Comparative Study

Abstract

The kernel is a non-parametric estimation method of the probability density function of a random variable based on a finite sample of data. The estimated function is smooth and level of smoothness is defined by a parameter represented by h, called bandwidth or window. In this simulation work we compare, by the use of mean square error and bias, the performance of the normal kernel in smoothing the empirical ROC curve, using various amounts of bandwidth. In this sense, we intend to compare the performance of the normal kernel, for various values of bandwidth, in the smoothing of ROC curves generated from Normal distributions and evaluate the variation of the mean square error for these samples. Two methodologies were followed: replacing the distribution functions of positive cases (abnormal) and negative (normal), on the definition of the ROC curve, smoothed by nonparametric estimators obtained via the kernel estimator and the smoothing applied directly to the ROC curve. We conclude that the empirical ROC curve has higher standard error when compared with the smoothed curves, a small value for the bandwidth favors a higher standard error and a higher value of the bandwidth increasing bias estimation.