Consistency of non parametric estimators of the area under the ROC curve

ABSTRACT

The area under the receiver operating characteristic (ROC) curve is a popular summary index that measures the accuracy of a continuous-scale diagnostic test to measure its accuracy. Under certain conditions on estimators of distribution functions, we prove a theorem on strong consistency of the non parametric “plugin” estimators of the area under the ROC curve. Based on this theorem, we construct some new “plugin” consistent estimators. The performance of the non parametric estimators considered is illustrated numerically and the estimators are compared in terms of bias, variance, and mean square error.

Keywords:

• ROC curve
• Estimation of AUC
• “Plugin” estimator
• Consistency
• Diagnostic test

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62G05, 62G07
• Secondary 62G20