$$D_s$$-optimality in copula models

Optimum experimental design theory has recently been extended for parameter estimation in copula models. The use of these models allows one to gain in flexibility by considering the model parameter set split into marginal and dependence parameters. However, this separation also leads to the natural issue of estimating only a subset of all model parameters. In this work, we treat this problem with the application of the \(D_s\)-optimality to copula models. First, we provide an extension of the corresponding equivalence theory. Then, we analyze a wide range of flexible copula models to highlight the usefulness of \(D_s\)-optimality in many possible scenarios. Finally, we discuss how the usage of the introduced design criterion also relates to the more general issue of copula selection and optimal design for model discrimination.