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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

  • Lopez, Olivier
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    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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    File URL: http://www.sciencedirect.com/science/article/pii/S0167668712000881
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    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
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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    1. Luciano, Elisa & Spreeuw, Jaap & Vigna, Elena, 2008. "Modelling stochastic mortality for dependent lives," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 234-244, October.
    2. 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, vol. 65(2), pages 457-471.
    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, vol. 66(2), pages 305-319.
    4. 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, vol. 33(2), pages 337-366.
    5. 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, vol. 32(4), pages 563-581.
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