Nonparametric and Semiparametric Optimal Transformations of Markers

• Activity Number: 126
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Chin-Tsang Chiang*+
• Companies: National Taiwan University
• Keywords: area between curve (ABC) ; area under curve (AUC) ; false positive rate (FPR) ; positive predictive value (PPV) ; receiver operating characteristic curve (ROC) ; true positive rate (TPR)

Abstract

The receiver operating characteristic (ROC) curve of a likelihood function has been shown to be the highest among all transformations of continuous markers. For any sampling scheme with the same likelihood function, the induced conditional probability is shown to be a strictly increasing function of likelihood function and is more flexible for analyzing ROC curves and theoretical development. To further compromise the difficult task of high-dimensionality in fully nonparametric models and the risk of fully parametric ones, an appealing single-index model with an unspecified link function is adopted in our optimization problem. Based on a nonparametric estimator of the area under the ROC curve (AUC), we develop the related inferences and provide some simple and easily checked conditions for the validity of asymptotic results.