A Semi-Parametric Copula Estimation under Censoring

This book combines two interesting branches of statistics: survival analysis and copula theory. The primary objective is to extend the copula theory results via semi-parametric estimation, under censored data. More precisely, we are interested by copulas semi-parametric estimates adapted for bivariate censored data. As theoretical results, general formulas were proved with analytical forms of the obtained estimators. The asymptotic normality of the empirical survival copula was established for the two censoring cases. The dependence structure between the bivariate survival times has been modeled under the assumption that the underlying copula is Archimedean. Accounting for various censoring patterns (singly or doubly censored).. We implemented the frailty model for two-variable survival data using Archimedean copulas in the final part of the book. The frailty variables considered here are latent and are nevertheless one-dimensional. In the example presented, this variable characterized the effect of the individual on the recurrence time. The applications for health-related survival data were next examined.