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Some mathematical properties of the ROC curve and their applications

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Abstract

In this paper we present ROC methodology and analyze the ROC curve. We describe first the historical background and its relation with signal detection theory. Some mathematical properties of this curve are given, and in particular the relation with stochastic orders and statistical hypotheses testing are described. We present also a medical application of the Neymann–Pearson lemma.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, via Cintia, Naples, Italy

    Camilla Calì & Maria Longobardi

Authors
  1. Camilla Calì
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  2. Maria Longobardi
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Correspondence to Maria Longobardi.

Additional information

Communicated by Salvatore Rionero.

Dedicated to the Memory of Carlo Ciliberto.

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Calì, C., Longobardi, M. Some mathematical properties of the ROC curve and their applications. Ricerche mat. 64, 391–402 (2015). https://doi.org/10.1007/s11587-015-0246-8

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  • DOI: https://doi.org/10.1007/s11587-015-0246-8

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