IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01141228.html
   My bibliography  Save this paper

Tree-based censored regression with applications in insurance

Author

Listed:
  • Olivier Lopez

    (LSTA - Laboratoire de Statistique Théorique et Appliquée - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche Scientifique)

  • Xavier Milhaud

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Pierre-Emmanuel Thérond

    (Galea & Associés, SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

We propose a regression tree procedure to estimate the conditional distribution of a variable which is not directly observed due to censoring. The model that we consider is motivated by applications in insurance , including the analysis of guarantees that involve durations, and claim reserving. We derive consistency results for our procedure, and for the selection of an optimal subtree using a pruning strategy. These theoretical results are supported by a simulation study, and two applications involving insurance datasets. The first concerns income protection insurance, while the second deals with reserving in third-party liability insurance.

Suggested Citation

  • Olivier Lopez & Xavier Milhaud & Pierre-Emmanuel Thérond, 2016. "Tree-based censored regression with applications in insurance," Post-Print hal-01141228, HAL.
    • Handle: RePEc:hal:journl:hal-01141228
    DOI: 10.1214/16-EJS1189
    Note: View the original document on HAL open archive server: https://hal.science/hal-01141228v2
    as

    Download full text from publisher

    File URL: https://hal.science/hal-01141228v2/document
    Download Restriction: no
    File URL: https://libkey.io/10.1214/16-EJS1189?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. César Sánchez Sellero & Wenceslao González Manteiga & Ingrid Van Keilegom, 2005. "Uniform Representation of Product‐Limit Integrals with Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 563-581, December.
    2. Wang, Huixia Judy & Wang, Lan, 2009. "Locally Weighted Censored Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1117-1128.
    3. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    4. Gao, Feng & Manatunga, Amita K. & Chen, Shande, 2004. "Identification of prognostic factors with multivariate survival data," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 813-824, May.
    5. Fan, Juanjuan & Nunn, Martha E. & Su, Xiaogang, 2009. "Multivariate exponential survival trees and their application to tooth prognosis," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1110-1121, February.
    6. Lopez, Olivier & Patilea, Valentin & Van Keilegom, Ingrid, 2013. "Single index regression models in the presence of censoring depending on the covariates," LIDAM Reprints ISBA 2013029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Sandrine Dudoit & Mark van der Laan & Sunduz Keles & Annette Molinaro & Sandra Sinisi & Siew Leng Teng, 2004. "Loss-Based Estimation with Cross-Validation: Applications to Microarray Data Analysis and Motif Finding," U.C. Berkeley Division of Biostatistics Working Paper Series 1136, Berkeley Electronic Press.
    8. Molinaro, Annette M. & Dudoit, Sandrine & van der Laan, M.J.Mark J., 2004. "Tree-based multivariate regression and density estimation with right-censored data," Journal of Multivariate Analysis, Elsevier, vol. 90(1), pages 154-177, July.
    9. Ali Gannoun & Jérôme Saracco & Ao Yuan & George E. Bonney, 2005. "Non‐parametric Quantile Regression with Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 527-550, December.
    10. Laan Mark J. van der & Dudoit Sandrine & Vaart Aad W. van der, 2006. "The cross-validated adaptive epsilon-net estimator," Statistics & Risk Modeling, De Gruyter, vol. 24(3), pages 373-395, December.
    11. Jérôme Saracco & A. Yuan & G.E. Bonney & Abdelmouhcine Gannoun, 2005. "Nonparametric quantille regression with censored data," Post-Print hal-00389170, HAL.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Farkas, Sébastien & Lopez, Olivier & Thomas, Maud, 2021. "Cyber claim analysis using Generalized Pareto regression trees with applications to insurance," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 92-105.
    2. Crevecoeur, Jonas & Robben, Jens & Antonio, Katrien, 2022. "A hierarchical reserving model for reported non-life insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 158-184.
    3. Marie Michaelides & Mathieu Pigeon & H'el`ene Cossette, 2022. "Individual Claims Reserving using Activation Patterns," Papers 2208.08430, arXiv.org, revised Aug 2023.
    4. Lopez, Olivier, 2019. "A censored copula model for micro-level claim reserving," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 1-14.
    5. Guillaume Coqueret & Tony Guida, 2020. "Training trees on tails with applications to portfolio choice," Annals of Operations Research, Springer, vol. 288(1), pages 181-221, May.
    6. Guillaume Coqueret & Tony Guida, 2020. "Training trees on tails with applications to portfolio choice," Post-Print hal-04144665, HAL.
    7. Gu, Zheng & Li, Yunxian & Zhang, Minghui & Liu, Yifei, 2023. "Modelling economic losses from earthquakes using regression forests: Application to parametric insurance," Economic Modelling, Elsevier, vol. 125(C).
    8. Yanez, Juan Sebastian & Pigeon, Mathieu, 2021. "Micro-level parametric duration-frequency-severity modeling for outstanding claim payments," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 106-119.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Olivier Lopez & Xavier Milhaud & Pierre-Emmanuel Thérond, 2015. "Tree-based censored regression with applications to insurance," Working Papers hal-01141228, HAL.
    2. García, A., 2016. "Oaxaca-Blinder Type Counterfactual Decomposition Methods for Duration Outcomes," Documentos de Trabajo 14186, Universidad del Rosario.
    3. Mercedes Conde‐Amboage & Ingrid Van Keilegom & Wenceslao González‐Manteiga, 2021. "A new lack‐of‐fit test for quantile regression with censored data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 655-688, June.
    4. Sungwan Bang & Soo-Heang Eo & Yong Mee Cho & Myoungshic Jhun & HyungJun Cho, 2016. "Non-crossing weighted kernel quantile regression with right censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(1), pages 100-121, January.
    5. Laan Mark J. van der & Dudoit Sandrine & Vaart Aad W. van der, 2006. "The cross-validated adaptive epsilon-net estimator," Statistics & Risk Modeling, De Gruyter, vol. 24(3), pages 373-395, December.
    6. Jacobo Uña-Álvarez & Noël Veraverbeke, 2013. "Generalized copula-graphic estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 343-360, June.
    7. Miguel A Delgado & Andrés García-Suaza & Pedro H C Sant’Anna, 2022. "Distribution regression in duration analysis: an application to unemployment spells [Lecture notes in statistics: Proceedings]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 675-698.
    8. Olivier Lopez & Valentin Patilea, 2007. "Nonparametric Lack-of-fit Tests for Parametric Mean-Regression Model with Censored Data," Working Papers 2007-01, Center for Research in Economics and Statistics.
    9. Lopez, O. & Patilea, V., 2009. "Nonparametric lack-of-fit tests for parametric mean-regression models with censored data," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 210-230, January.
    10. Wei-Yin Loh, 2014. "Fifty Years of Classification and Regression Trees," International Statistical Review, International Statistical Institute, vol. 82(3), pages 329-348, December.
    11. Worku Biyadgie Ewnetu & Irène Gijbels & Anneleen Verhasselt, 2024. "Two-piece distribution based semi-parametric quantile regression for right censored data," Statistical Papers, Springer, vol. 65(5), pages 2775-2810, July.
    12. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    13. Gribkova, Svetlana, 2015. "Vector quantization and clustering in the presence of censoring," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 220-233.
    14. de Uña Álvarez, Jacobo & Roca Pardiñas, Javier, 2009. "Additive models in censored regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3490-3501, July.
    15. Xie, Shangyu & Wan, Alan T.K. & Zhou, Yong, 2015. "Quantile regression methods with varying-coefficient models for censored data," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 154-172.
    16. Manda, Julius & Feleke, Shiferaw & Mutungi, Christopher & Tufa, Adane H. & Mateete, Bekunda & Abdoulaye, Tahirou & Alene, Arega D., 2024. "Assessing the speed of improved postharvest technology adoption in Tanzania: The role of social learning and agricultural extension services," Technological Forecasting and Social Change, Elsevier, vol. 202(C).
    17. Narisetty, Naveen & Koenker, Roger, 2022. "Censored quantile regression survival models with a cure proportion," Journal of Econometrics, Elsevier, vol. 226(1), pages 192-203.
    18. Bucher, Axel & El Ghouch, Anouar & Van Keilegom, Ingrid, 2014. "Single-index quantile regression models for censored data," LIDAM Discussion Papers ISBA 2014001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Eliana Christou & Michael G. Akritas, 2019. "Single index quantile regression for censored data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 655-678, December.
    20. Liang, Weijuan & Zhang, Qingzhao & Ma, Shuangge, 2024. "Hierarchical false discovery rate control for high-dimensional survival analysis with interactions," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-01141228. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.