Analysis of spatially correlated functional data objects

Alghamdi, Salihah Safar (2019) Analysis of spatially correlated functional data objects. PhD thesis, University of Glasgow.

Abstract

Space-time data are of great interest in many fields of research, but they are inherently complex in nature which leads to practical issues when formulating statistical models to analyse them. In classical analysis of space-time data the temporal variation is modelled using traditional time-series analysis. This thesis focuses on build- ing a comprehensive framework for analysing space-time data, where the temporal component is considered to be a continuous function and modelled using functional data analytic tools. There are several approaches for analysis spatially correlated functional data, but most of them are designed for specific applications and there is no easy way of comparing these methods. In summary, the challenge in modelling space-time data using functional data analytic techniques is that there is no clear rule regarding which method is most appropriate for analysing a new dataset. Existing methods have been developed for specific applications without giving a clear indication for a practitioner regarding their appropriateness. This motivates us to propose a clear flow chart of the analysis of space-time data using functional data analysis methods and develop a framework under which different existing methods can be compared.
In this research, we provide a clear comparison between two widely different methods of modelling spatial dependence one using parametric and the other using non-parametric spatial dependence. These techniques were developed for datasets with different complexities. First, we had to generalise the methodologies and codes of both of these methods to analyse data with features they were not originally designed for. We then compared the performance of these two methods on two real life datasets, the enhanced vegetation index (EVI) data and the electroencephalography (EEG) data. Further we have generalised our framework to accommodate replicated data and used it to build classification tools that outperforms all existing approaches.
One major contribution of this thesis is the development of the methodological framework and computational tool for the analysis of spatially correlated functional data. We have also clearly demonstrated, theoretically, and through simulations that our approach outperforms existing methods. Finally, for the EEG data we have demonstrated that classification tools built on representations from our models can outperform classification tools using the raw data.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: H Social Sciences > HA Statistics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Supervisor's Name: Ray, Dr. Surajit
• Date of Award: 2019
• Depositing User: Mrs Salihah Alghamdi
• Unique ID: glathesis:2019-71942
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 14 Jun 2019 08:14
• Last Modified: 05 Mar 2020 22:46
• Thesis DOI: 10.5525/gla.thesis.71942
• URI: https://theses.gla.ac.uk/id/eprint/71942