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Distortion risk measures, ROC curves, and distortion divergence

  • Johannes M. Schumacher ORCID logo EMAIL logo
Veröffentlicht/Copyright: 11. November 2017
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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.

MSC 2010: 62P05; 60B10

Acknowledgements

The author gratefully acknowledges comments by two anonymous reviewers, which helped improve the paper.

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Received: 2017-4-21
Revised: 2017-10-18
Accepted: 2017-10-19
Published Online: 2017-11-11
Published in Print: 2018-1-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 21.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/strm-2017-0012/pdf
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