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Distortion risk measures, ROC curves, and distortion divergence

Johannes Schumacher

Statistics & Risk Modeling, 2018, vol. 35, issue 1-2, 35-50

Abstract: Distortion functions are employed to define measures of risk. Receiver operating characteristic (ROC) curves are used to describe the performance of parametrized test families in testing a simple null hypothesis against a simple alternative. This paper provides a connection between distortion functions on the one hand, and ROC curves on the other. This leads to a new interpretation of some well-known classes of distortion risk measures, and to a new notion of divergence between probability measures.

Keywords: Risk measures; hypothesis testing; receiver operating characteristic; divergence; 62P05; 60B10 (search for similar items in EconPapers)
Date: 2018
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