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On the joint asymptotic behavior of two rank-based estimators of the association parameter in the gamma frailty model

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  • Genest, Christian
  • Quessy, Jean-François
  • Rémillard, Bruno

Abstract

Rank-based estimators were proposed by Clayton [Clayton D.G., 1978. A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65, 141-151.] and Oakes [Oakes, D., 1982. A model for association in bivariate survival data. J. Roy. Statist. Soc. Ser. B 44, 414-422.] for the association parameter in the bivariate gamma frailty model. The joint asymptotic behavior of these estimators is considered here, following a different approach from that used by Oakes [Oakes, D., 1982. A model for association in bivariate survival data. J. Roy. Statist. Soc. Ser. B 44, 414-422; Oakes, D., 1986. Semiparametric inference in a model for association in bivariate survival data. Biometrika 73, 353-361]. This leads to a correction of the formula given by Shih [Shih, J.H. 1998. A goodness-of-fit test for association in a bivariate survival model. Biometrika 85, 189-200.] for the limiting covariance between the two estimators.

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  • Genest, Christian & Quessy, Jean-François & Rémillard, Bruno, 2006. "On the joint asymptotic behavior of two rank-based estimators of the association parameter in the gamma frailty model," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 10-18, January.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:1:p:10-18
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    References listed on IDEAS

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    1. Wenqing He & Jerald F. Lawless, 2003. "Flexible Maximum Likelihood Methods for Bivariate Proportional Hazards Models," Biometrics, The International Biometric Society, vol. 59(4), pages 837-848, December.
    2. Weijing Wang, 2003. "Estimating the association parameter for copula models under dependent censoring," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 257-273, February.
    3. Genest, Christian & Rivest, Louis-Paul, 2001. "On the multivariate probability integral transformation," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 391-399, July.
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    Cited by:

    1. Daniel Berg & Jean‐François Quessy, 2009. "Local Power Analyses of Goodness‐of‐fit Tests for Copulas," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 389-412, September.
    2. Nasri, Bouchra R., 2022. "Tests of serial dependence for multivariate time series with arbitrary distributions," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    3. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions. III," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 24(4), pages 100-130.
    4. Lajmi Lakhal & Louis-Paul Rivest & Belkacem Abdous, 2008. "Estimating Survival and Association in a Semicompeting Risks Model," Biometrics, The International Biometric Society, vol. 64(1), pages 180-188, March.
    5. Kojadinovic, Ivan & Yan, Jun, 2010. "Comparison of three semiparametric methods for estimating dependence parameters in copula models," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 52-63, August.
    6. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.

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