Parametric estimation of conditional Archimedean copula generators for censored data

Abstract: In this paper, we propose a novel approach for estimating Archimedean copula generators in a conditional setting, incorporating endogenous variables. Our method allows for the evaluation of the impact of the different levels of covariates on both the strength and shape of dependence by directly estimating the generator function rather than the copula itself. As such, we contribute to relaxing the simplifying assumption inherent in traditional copula modeling. We demonstrate the effectiveness of our methodology through applications in two diverse settings: a diabetic retinopathy study and a claims reserving analysis. In both cases, we show how considering the influence of covariates enables a more accurate capture of the underlying dependence structure in the data, thus enhancing the applicability of copula models, particularly in actuarial contexts.