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

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.