Inferences on the Association Parameter in Copula Models for Bivariate Survival Data

TLDR

The study investigates two‑stage parametric and semi‑parametric estimation procedures for the association parameter in copula models for bivariate survival data with censoring, and proposes a consistent variance estimator for the semi‑parametric estimator. The authors derive asymptotic properties of these estimators, compare their performance through simulations, and illustrate the methods on an AIDS dataset. Both estimators are efficient at independence, and margin parameter estimates are highly efficient and robust to misspecified dependency structures.

Abstract

We investigate two-stage parametric and two-stage semi-parametric estimation procedures for the association parameter in copula models for bivariate survival data where censoring in either or both components is allowed. We derive asymptotic properties of the estimators and compare their performance by simulations. Both parametric and semi-parametric estimators of the association parameter are efficient at independence, and the parameter estimates in the margins have high efficiency and are robust to misspecification of dependency structures. In addition, we propose a consistent variance estimator for the semi-parametric estimator of the association parameter. We apply the proposed methods to an AIDS data set for illustration.