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Testing for auto-calibration with Lorenz and Concentration curves

Author

Listed:
  • Denuit, Michel
  • Huyghe, Julie
  • Trufin, Julien
  • Verdebout, Thomas

Abstract

Dominance relations and diagnostic tools based on Lorenz and Concentration curves in order to compare competing estimators of the regression function have recently been proposed. This approach turns out to be equivalent to forecast dominance when the estimators under consideration are auto-calibrated. A new characterization of auto-calibration is established, based on the graphs of Lorenz and Concentration curves. This result is exploited to propose an effective testing procedure for auto-calibration. A simulation study is conducted to evaluate its performances and its relevance for practice is demonstrated on an insurance data set.

Suggested Citation

  • Denuit, Michel & Huyghe, Julie & Trufin, Julien & Verdebout, Thomas, 2024. "Testing for auto-calibration with Lorenz and Concentration curves," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 130-139.
  • Handle: RePEc:eee:insuma:v:117:y:2024:i:c:p:130-139
    DOI: 10.1016/j.insmatheco.2024.04.003
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    References listed on IDEAS

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    1. Michel Denuit & Arthur Charpentier & Julien Trufin, 2021. "Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning," Papers 2103.03635, arXiv.org, revised Jul 2021.
    2. Werner Ehm & Tilmann Gneiting & Alexander Jordan & Fabian Krüger, 2016. "Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 505-562, June.
    3. Denuit, Michel & Charpentier, Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 485-497.
    4. Frees, Edward W. & Meyers, Glenn & Cummings, A. David, 2011. "Summarizing Insurance Scores Using a Gini Index," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1085-1098.
    5. Gribkova, N.V. & Su, J. & Zitikis, R., 2022. "Inference for the tail conditional allocation: Large sample properties, insurance risk assessment, and compound sums of concomitants," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 199-222.
    6. Denuit, Michel & Charpentier , Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," LIDAM Reprints ISBA 2021049, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Xuehu Zhu & Xu Guo & Lu Lin & Lixing Zhu, 2016. "Testing for positive expectation dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 135-153, February.
    8. 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.
    9. M. Lindholm & F. Lindskog & J. Palmquist, 2023. "Local bias adjustment, duration-weighted probabilities, and automatic construction of tariff cells," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2023(10), pages 946-973, November.
    10. Ciatto, Nicolas & Verelst, Harrison & Trufin, Julien & Denuit, Michel, 2023. "Does autocalibration improve goodness of lift?," LIDAM Reprints ISBA 2023007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    12. Denuit, Michel & Charpentier, Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," LIDAM Discussion Papers ISBA 2021013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Denuit, Michel & Trufin, Julien & Verdebout, Thomas, 2021. "Testing for more positive expectation dependence with application to model comparison," LIDAM Reprints ISBA 2021048, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Denuit, Michel & Trufin, Julien & Verdebout, Thomas, 2021. "Testing for more positive expectation dependence with application to model comparison," LIDAM Discussion Papers ISBA 2021021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. 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).
    16. 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).
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    More about this item

    Keywords

    Concentration curve; Lorenz curve; Integrated Concentration Curve (ICC); Area Between the Curves (ABC); Gini coefficient; Auto-calibrated estimators;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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