Title: Predictive inference for bivariate data using nonparametric copula
Authors: Tahani Coolen-Maturi - Durham University (United Kingdom) [presenting]
Abstract: A new method is presented for prediction of an event involving a future bivariate observation. The method combines nonparametric predictive inference (NPI) applied to the marginals with a nonparametric copula to model and estimate the dependence structure between two random quantities, as such the method is fully nonparametric. In NPI, uncertainty is quantified through imprecise probabilities. Several novel aspects of statistical inference are presented. First, the link between NPI and copulas is powerful and attractive with regard to computation. Secondly, statistical methods using imprecise probability have gained substantial attention in recent years, where typically imprecision is used on aspects for which less information is available. A different approach, namely imprecision mainly being introduced on the marginals, is presented for which there is typically quite sufficient information, in order to provide robustness for the harder part of the inference, namely the dependence structure. Thirdly, the set-up of the simulations to evaluate the performance of the proposed method is novel, key to these are frequentist comparisons of the success proportion of predictions with the corresponding data-based lower and upper predictive inferences. All these novel ideas can be applied far more generally to other inferences and models.