Properties of the marginal survival functions for dependent censored data under an assumed Archimedean copula

Given a dependent censored data (X, δ) = (min(T, C), I(T < C)) from an Archimedean copula model, we give general formulas for possible marginal survival functions of T and C. Based on our formulas, we can easily establish the relationship between all these survival functions and derive some useful identifiability results. Also based on our formulas, we propose a new estimator of the marginal survival function when the Archimedean copula model is assumed to be known. Simulation studies have shown that our estimator is comparable with the copula-graphic estimator proposed by Zheng and Klein (1995) and Zheng and Klein's estimator (1994). We illustrate the application of our estimator using a survival data set and end our talk with some discussions.