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Testing for more positive expectation dependence with application to model comparison

Author

Listed:
  • Denuit, Michel

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

  • Trufin, Julien

    (ULB)

  • Verdebout, Thomas

    (ULB)

Abstract

Modern data science tools are effective to produce predictions that strongly correlate with responses. Model comparison can therefore be based on the strength of dependence between responses and their predictions. Positive expectation dependence turns out to be attractive in that respect. The present paper proposes an effective testing procedure for this dependence concept and applies it to model selection. A simulation study is performed to evaluate the performances of the proposed testing procedure. Empirical illustrations using insurance loss data demonstrate the relevance of the approach for model selection in supervised learning. The most positively expectation dependent predictor can then be autocalibrated to obtain its balance-corrected version that appears to be optimal with respect to Bregman, or forecast dominance.

Suggested Citation

  • 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).
    • Handle: RePEc:aiz:louvad:2021021
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    References listed on IDEAS

    as
    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. Michel Denuit & Louis Eeckhoudt, 2016. "Risk aversion, prudence, and asset allocation: a review and some new developments," Theory and Decision, Springer, vol. 80(2), pages 227-243, February.
    3. Oliver Linton & Yoon Jae Whang & Yu-Min Yen, 2021. "The lower regression function and testing expectation dependence dominance hypotheses," Econometric Reviews, Taylor & Francis Journals, vol. 40(8), pages 709-727, September.
    4. Li, Jingyuan & Liu, Dongri & Wang, Jianli, 2016. "Risk aversion with two risks: A theoretical extension," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 100-105.
    5. Michel Denuit & Louis Eeckhoudt, 2016. "Risk aversion, prudence, and asset allocation: a review and some new developments," Theory and Decision, Springer, vol. 80(2), pages 227-243, February.
    6. Edward W. (Jed) Frees & Glenn Meyers & A. David Cummings, 2014. "Insurance Ratemaking and a Gini Index," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(2), pages 335-366, June.
    7. Guo, Xu & Li, Jingyuan, 2016. "Confidence band for expectation dependence with applications," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 141-149.
    8. Denuit, Michel & Hainaut, Donatien & Trufin, Julien, 2020. "Effective Statistical Learning Methods for Actuaries II : Tree-Based Methods and Extensions," LIDAM Reprints ISBA 2020035, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. 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).
    10. Soon Koo Hong & Keun Ock Lew & Richard MacMinn & Patrick Brockett, 2011. "Mossin's Theorem Given Random Initial Wealth," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(2), pages 309-324, June.
    11. 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).
    12. Denuit, Michel, 2010. "Positive dependence of signals," LIDAM Discussion Papers ISBA 2010025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Denuit, Michel M. & Mesfioui, Mhamed, 2017. "Preserving the Rothschild–Stiglitz type increase in risk with background risk: A characterization," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 1-5.
    14. 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).
    15. 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.
    16. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    17. Denuit, Michel & Eeckhoudt, Louis, 2016. "Risk aversion, prudence, and asset allocation : a review and some new developments," LIDAM Reprints ISBA 2016009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. 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.
    19. 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.
    20. Denuit, Michel & Mesfioui, Mhamed, 2017. "Preserving the Rothschild–Stiglitz type increase in risk with background risk: A characterization," LIDAM Reprints ISBA 2017002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    21. Juan-JosÈ Ganuza & JosÈ S. Penalva, 2010. "Signal Orderings Based on Dispersion and the Supply of Private Information in Auctions," Econometrica, Econometric Society, vol. 78(3), pages 1007-1030, May.
    22. 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).
    23. Li, Jingyuan, 2011. "The demand for a risky asset in the presence of a background risk," Journal of Economic Theory, Elsevier, vol. 146(1), pages 372-391, January.
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    Keywords

    Expectation dependence ; concentration curve ; Lorenz curve ; autocalibration ; convex order ; balance correction;
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