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

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  • Denuit, Michel

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Trufin, Julien

    (Université Libre de Bruxelles)

Abstract

Wüthrich (2022) 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.

Suggested Citation

  • Denuit, Michel & Trufin, Julien, 2022. "Model selection with Pearson’s correlation, concentration and Lorenz curves under autocalibration," LIDAM Discussion Papers ISBA 2022033, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2022033
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    References listed on IDEAS

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    1. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    2. Denuit, Michel & Trufin, Julien, 2021. "Lorenz curve, Gini coefficient, and Tweedie dominance for autocalibrated predictors," LIDAM Discussion Papers ISBA 2021036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," LIDAM Reprints ISBA 2019046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 128-139.
    5. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," LIDAM Discussion Papers ISBA 2019006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Fabian Krüger & Johanna F. Ziegel, 2021. "Generic Conditions for Forecast Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 972-983, October.
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    Cited by:

    1. Denuit, Michel & Trufin, Julien, 2022. "Autocalibration by balance correction in nonlife insurance pricing," LIDAM Discussion Papers ISBA 2022041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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