Model selection with Pearson’s correlation, concentration and Lorenz curves under autocalibration

Michel Denuit and Julien Trufin
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Michel Denuit: Université catholique de Louvain, LIDAM/ISBA, Belgium
Julien Trufin: Université Libre de Bruxelles

No 2023025, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: Wüthrich (Eur Actuar J, https://doi.org/10.1007/s13385-022-00339-9, 2023) established that the Gini index is a consistent scoring rule in the class of autocalibrated predictors. This note further explores performances criteria in this class. Elementary Pearson’s correlation turns out to be consistent when restricted to autocalibrated predictors. Also, any performance measure that is minimized for predictors that are comonotonic with the true regression model is consistent under autocalibration. This provides a new proof of the consistency for Gini index. In addition, it is established that the concentration curve of the true model is the lowest possible concentration curve under autocalibration and that the same property holds true for Lorenz curve.

Keywords: Gini index; Consistent loss function; Autocalibration; Concentration curve; Comonotonicity (search for similar items in EconPapers)
Pages: 8
Date: 2023-05-26
Note: In: European Actuarial Journal, 2023, vol. 13(2), p. 871-878
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2023025

DOI: 10.1007/s13385-023-00353-5

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