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Robust estimates of insurance misrepresentation through kernel quantile regression mixtures

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  • Hong Li
  • Qifan Song
  • Jianxi Su

Abstract

This paper pertains to a class of nonparametric methods for studying the misrepresentation issue in insurance applications. For this purpose, mixture models based on quantile regression in reproducing kernel Hilbert spaces are employed. Compared with the existing parametric approaches, the proposed framework features a more flexible statistics structure which could alleviate the risk of model misspecification, and is in the meantime more robust to outliers in the data. The proposed framework can not only estimate the prevalence of misrepresentation in the data, but also help identify the most suspicious individuals for the validation purpose. Through embedding state‐of‐the‐art machine learning techniques, we present a novel statistics procedure to efficiently estimate the proposed misrepresentation model in the presence of massive data. The proposed methodology is applied to study the Medical Expenditure Panel Survey data, and a significant degree of misrepresentation activity is found on the self‐reported insurance status.

Suggested Citation

  • Hong Li & Qifan Song & Jianxi Su, 2021. "Robust estimates of insurance misrepresentation through kernel quantile regression mixtures," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(3), pages 625-663, September.
    • Handle: RePEc:bla:jrinsu:v:88:y:2021:i:3:p:625-663
    DOI: 10.1111/jori.12358
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    1. Paul Embrechts & Marius Hofert, 2013. "A note on generalized inverses," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 423-432, June.
    2. Andrea Gabrielli & Mario V. Wüthrich, 2018. "An Individual Claims History Simulation Machine," Risks, MDPI, vol. 6(2), pages 1-32, March.
    3. Fabio Baione & Davide Biancalana, 2019. "An Individual Risk Model for Premium Calculation Based on Quantile: A Comparison between Generalized Linear Models and Quantile Regression," North American Actuarial Journal, Taylor & Francis Journals, vol. 23(4), pages 573-590, October.
    4. Ana M. Pérez-Marín & Montserrat Guillen & Manuela Alcañiz & Lluís Bermúdez, 2019. "Quantile Regression with Telematics Information to Assess the Risk of Driving above the Posted Speed Limit," Risks, MDPI, vol. 7(3), pages 1-11, July.
    5. S. M. Schennach & Yingyao Hu, 2013. "Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 177-186, March.
    6. Susanne M. Schennach, 2016. "Recent Advances in the Measurement Error Literature," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 341-377, October.
    7. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
    8. Michelle Xia, 2018. "Bayesian Adjustment for Insurance Misrepresentation in Heavy-Tailed Loss Regression," Risks, MDPI, vol. 6(3), pages 1-16, August.
    9. John Cawley & Chad Meyerhoefer & Adam Biener & Mette Hammer & Neil Wintfeld, 2015. "Savings in Medical Expenditures Associated with Reductions in Body Mass Index Among US Adults with Obesity, by Diabetes Status," PharmacoEconomics, Springer, vol. 33(7), pages 707-722, July.
    10. Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
    11. Yuan, Ming, 2006. "GACV for quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 813-829, February.
    12. Akakpo, Rexford M. & Xia, Michelle & Polansky, Alan M., 2019. "Frequentist Inference In Insurance Ratemaking Models Adjusting For Misrepresentation," ASTIN Bulletin, Cambridge University Press, vol. 49(1), pages 117-146, January.
    13. Bhattacharya, Jay & Bundorf, M. Kate, 2009. "The incidence of the healthcare costs of obesity," Journal of Health Economics, Elsevier, vol. 28(3), pages 649-658, May.
    14. Wu, Qiang & Yao, Weixin, 2016. "Mixtures of quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 162-176.
    15. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, May.
    16. Helmut Küchenhoff & Samuel M. Mwalili & Emmanuel Lesaffre, 2006. "A General Method for Dealing with Misclassification in Regression: The Misclassification SIMEX," Biometrics, The International Biometric Society, vol. 62(1), pages 85-96, March.
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    1. Michele Tumminello & Andrea Consiglio & Pietro Vassallo & Riccardo Cesari & Fabio Farabullini, 2023. "Insurance fraud detection: A statistically validated network approach," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(2), pages 381-419, June.
    2. Daniel Bauer & James Tyler Leverty & Joan Schmit & Justin Sydnor, 2021. "Symposium on insure‐tech, digitalization, and big‐data techniques in risk management and insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(3), pages 525-528, September.

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