Parametric estimation of conditional Archimedean copula generators for censored data

A novel framework is introduced for estimating Archimedean copula generators in a conditional setting by embedding endogenous variables directly within the generator function. Unlike standard copula constructions that rely on a fixed dependence structure across all covariate levels, the proposed methodology allows both the strength and the shape of dependence to evolve with the covariates. To identify the values of a continuous risk factor at which the dependence pattern undergoes substantive changes, an iterative splitting algorithm is developed to determine optimal partitioning points within the covariate range. The approach is evaluated through applications to a diabetic retinopathy study and a claims reserving analysis, illustrating that explicitly modelling covariate effects yields a more accurate representation of dependence and enhances the practical relevance of copula models in medical and actuarial settings.