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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.

Suggested Citation

  • 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. 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.
    2. 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. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    3. 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.
    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. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions. III," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 24(4), pages 100-130.

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