ALMASOUD, TAGHREED (2025) Nonparametric Predictive Inference for Multivariate Data using Copulas. Doctoral thesis, Durham University.
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Abstract
Modelling dependence among random quantities is a core aspect of multivariate data analysis. Copulas provide a flexible and powerful approach to capturing the dependence structure between random quantities. Several dependence models have been proposed in the literature, including classical copulas, vine copulas, and fully nested Archimedean copulas (FNAC). In parallel, several statistical methods have been developed within the imprecise probability framework, including nonparametric predictive inference (NPI). NPI is based on minimal modelling assumptions and quantifies uncertainty using lower and upper probabilities. Recently, NPI has been applied to bivariate data using both parametric and nonparametric copulas.
This thesis contributes to the use of NPI for multivariate data by presenting different approaches for prediction. The focus is on copulas for modelling dependence, as they provide high flexibility for modelling complex dependency patterns. A generalization is proposed for the method that combines NPI with bivariate data, using a parametric copula with a single parameter to model dependence. The approach is further extended by introducing a fully nonparametric version that uses a nonparametric copula. A novel method for combining NPI with vine copulas is also presented, motivated by the vine copulas ability to capture several dependence structures in a model. In addition, a new method integrating NPI with FNAC is developed, where FNAC is a promising model for capturing different dependencies within a model using Archimedean copulas. The proposed methods are illustrated using examples from the literature. Simulation studies are conducted to evaluate the predictive performance of the proposed methods and to compare the methods, highlighting their strengths and differences. The results indicate that the methods with either vine copulas or FNAC perform well compared to other methods.
Item Type: | Thesis (Doctoral) |
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Award: | Doctor of Philosophy |
Faculty and Department: | Faculty of Science > Mathematical Sciences, Department of |
Thesis Date: | 2025 |
Copyright: | Copyright of this thesis is held by the author |
Deposited On: | 28 Jul 2025 13:10 |