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A generalization of the Kaplan–Meier estimator for analyzing bivariate mortality under right-censoring and left-truncation with applications in model-checking for survival copula models

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  • Lopez, Olivier
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    Abstract

    In this paper we provide a new nonparametric estimator of the joint distribution of two lifetimes under random right censoring and left truncation which can be seen as a bivariate extension of the Kaplan–Meier estimator. We derive asymptotic results for this estimator, including uniform n1/2-consistency, and develop a general methodology for bivariate lifetime modeling, a critical issue in studying reversion conditions that are commonplace in defined benefit pensions and private annuity contracts. An application to goodness-of-fit for survival copula models is discussed. We show that the procedures that we use are consistent, and propose a bootstrap procedure based on our estimator to compute the critical values. The new technique that we propose is tested on the Canadian dataset initially studied by Frees et al. (1996).

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 51 (2012)
    Issue (Month): 3 ()
    Pages: 505-516

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    Handle: RePEc:eee:insuma:v:51:y:2012:i:3:p:505-516

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Kaplan–Meier estimator; Bivariate censoring; Left-truncation; Mortality analysis; Lifetime analysis; Nonparametric estimation; Copula models; Bootstrap;

    References

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    1. Luciano, Elisa & Spreeuw, Jaap & Vigna, Elena, 2008. "Modelling stochastic mortality for dependent lives," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 43(2), pages 234-244, October.
    2. César Sánchez Sellero & Wenceslao González Manteiga & Ingrid 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, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 563-581.
    3. Ross L. Prentice & F. Zoe Moodie & Jianrong Wu, 2004. "Hazard-based nonparametric survivor function estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 66(2), pages 305-319.
    4. Michael G. Akritas & Ingrid Van Keilegom, 2003. "Estimation of bivariate and marginal distributions with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 65(2), pages 457-471.
    5. Christian Genest & Jean-François Quessy & Bruno Rémillard, 2006. "Goodness-of-fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 337-366.
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    Cited by:
    1. Alemany, Ramon & Bolancé, Catalina & Guillén, Montserrat, 2013. "A nonparametric approach to calculating value-at-risk," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 52(2), pages 255-262.
    2. Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2014. "Accounting for severity of risk when pricing insurance products," Working Papers, Universitat de Barcelona, UB Riskcenter 2014-05, Universitat de Barcelona, UB Riskcenter.

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