Predictive inference for bivariate data: Combining nonparametric predictive inference for marginals with an estimated copula

Abstract

ABSTRACTThis article presents a new method for prediction of an event involving a future bivariate observation. The method combines nonparametric predictive inference (NPI) applied to the marginals with a parametric copula to model and estimate the dependence structure between two random quantities, as such, the method is semiparametric. In NPI, uncertainty is quantified through imprecise probabilities. The resulting imprecision in the marginals provides robustness with regard to the assumed parametric copula. Due to the specific nature of NPI, the estimation of the copula parameter is also quite straightforward. The performance of this method is investigated via simulations, with particular attention to robustness with regard to the assumed copula in case of small data sets. The method is further illustrated via two examples, using small data sets from the literature. This article presents several novel aspects of statistical inference. First, the link between NPI and copulas is powerful and attractive w...