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
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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- 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.
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- Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2007. "Modelling Stochastic Mortality for Dependent Lives," CeRP Working Papers 58, Center for Research on Pensions and Welfare Policies, Turin (Italy).
- 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.
- 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.
- 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.
- 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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