Likelihood Ratio Test in the Correlated Gamma-Frailty Model

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Abstract
The correlated gamma-frailty model is a generalization of Cox' proportional hazard model, which allows for correlation between individuals within the same group. The nonparametric maximum likelihood estimator in this model has previously been studied by Murphy (1994, 1995) and Parner (1998). Here we show that the likelihood ratio test can be performed with the cf2 distribution as asymptotic law, with the degrees of freedom f equal to the number of Euclidean parameters fixed under the hypothesis. As a side effect we also have a new proof for asymptotic normality and efficiency of the Euclidean component of the maximum likelihood parameter. Finally, we show how standard errors can be computed.