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Consider the estimation of the survival function S of a survival time Y that is subject to random right censoring via a censoring time C. The common assumption of independence between Y and C is often not verified in practice. In order to circumvent this problem, Rivest and Wells (2001) supposed that the relation between Y and C is given by a known copula, and they proposed an estimator of S under this assumption. The drawback of their approach is however that the copula needs to be known, which is often unrealistic in practice. In fact, it is in general not possible to estimate the copula when only repeated observations of min(Y,C) and I(Y <= C) are available.

In this paper, we propose an estimator of S when the Archimedean copula of (Y,C) is not supposed to be known. This is achieved by assuming that both Y and C are subject to a second censoring time D, which is assumed to be independent of (Y,C). The identifiability of the proposed model is established, we obtain the asymptotic normality of the estimator of the copula, we perform simulations to verify the behavior of our proposed estimation procedure, and we apply our method to real data coming from a study on Hodgkin's disease.

*Speaker:* Ingrid Van Keilegom (Institut de statistique, Université catholique de Louvain, Louvain-la-Neuve, Belgium)

*When and where?*

Tuesday, Mar 15, 2011, 4.30 pm, M / E25

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