Concentration and ROC Curves, Revisited

Mauro Gasparini () and Lidia Sacchetto
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Mauro Gasparini: Politecnico di Torino
Lidia Sacchetto: Politecnico di Torino

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 1, No 11, 292-305

Abstract: Abstract This work is aimed at illustrating the strict relationship between a general definition of concentration function appeared quite some time ago on this journal and a widely used measure of the diagnostic strength of a family of binary classifiers indexed by a threshold parameter, the so-called ROC curve. The ROC curve is a common work tool in Statistics, Machine Learning and Artificial Intelligence, appearing in many applications where a binary classification (diagnosis) procedure is of interest. Hence, it is worth remarking that diagnostic strength and concentration are two sides of the same coin: the higher the concentration of one probability measure with respect to another, the higher the diagnostic strength of the likelihood ratio classification rule.

Keywords: Likelihood ratio; Neyman-Pearson lemma; Classification.; 62H30; 62H20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13171-021-00244-5

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