Smoothing spline for the AUC estimate: Simulation studies in Gaussian data

Receiver operating characteristic (ROC) curve has been employed in classification problems along with the area under the curve (AUC) as the performance indicator of classifiers. Both parametric and non-parametric methods have been widely used to estimate the ROC curve as well as the AUC. In this study, a smoothing spline is proposed in order to provide an alternative of the ROC curve and AUC estimate. A logistic regression is selected as a base classifier for simulation cases of Gaussian and mixture of Gaussian data. The smoothing spline, bi-normal model and empirical method are compared in terms of root mean square error (RMSE) from the true ROC curve and the bias from the true AUC. The results indicate that the ROC curve and its AUC obtained from smoothing spline can provide a trade-off between the parametric bi-normal model and non-parametric empirical method, with 1.4% of bias and 7.75 of RMSE, on average for a dichotomous classification.