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

• Published in: European actuarial journal Vol. 13; no. 2; pp. 871 - 878
• Main Authors: Denuit, Michel, Trufin, Julien
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-12-2023; Springer Nature B.V
• Subjects: Adverse selection; Applications of Mathematics; Economics; Equality; Financial Services; Game Theory; Letter; Machine learning; Mathematics; Mathematics and Statistics; Policyholders; Quantitative Finance; Random variables; Social and Behav. Sciences; Consistent loss function; Concentration curve; Gini index; Comonotonicity; Autocalibration
• ISSN: 2190-9733; 2190-9741
• DOI: 10.1007/s13385-023-00353-5

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.