- Volume 48 Issue 3
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NONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION OF A CONCAVE RECEIVER OPERATING CHARACTERISTIC CURVE VIA GEOMETRIC PROGRAMMING
- Lee, Kyeong-Eun (Department of Statistics Kyungpook National University) ;
- Lim, Johan (Department of Statistics Seoul National University)
- Received : 2009.09.16
- Published : 2011.05.31
A receiver operating characteristic (ROC) curve plots the true positive rate of a classier against its false positive rate, both of which are accuracy measures of the classier. The ROC curve has several interesting geometrical properties, including concavity which is a necessary condition for a classier to be optimal. In this paper, we study the nonparametric maximum likelihood estimator (NPMLE) of a concave ROC curve and its modification to reduce bias. We characterize the NPMLE as a solution to a geometric programming, a special type of a mathematical optimization problem. We find that the NPMLE is close to the convex hull of the empirical ROC curve and, thus, has smaller variance but positive bias at a given false positive rate. To reduce the bias, we propose a modification of the NPMLE which minimizes the
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