Date of Award

Summer 2015

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

Norou Diawara

Committee Member

N. Rao Chaganty

Committee Member

Michael J. Doviak

Committee Member

Khan M. Iftekharuddin

Abstract

Statistical classification is a field of study that has developed significantly after 1960's. This research has a vast area of applications. For example, pattern recognition has been proposed for automatic character recognition, medical diagnostic and most recently in data mining. Classical discrimination rule assumes normality. However in many situations, this assumption is often questionable. In fact for some data, the pattern vector is a mixture of discrete and continuous random variables. In this dissertation, we use copula densities to model class conditional distributions. Such types of densities are useful when the marginal densities of a pattern vector are not normally distributed. This type of models are also useful for a mixed discrete and continuous feature types. Finite mixture density models are very flexible in building classifier and clustering, and for uncovering hidden structures in the data. We use finite mixture Gaussian copula and copula of the Archimedean family based mixture densities to build classifier. The complexities of the estimation are presented. Under such mixture models, maximum likelihood estimation methods are not suitable and regular expectation maximization algorithm may not converge, and if it does, not efficiently. We propose a new estimation method to evaluate such densities and build the classifier based on finite mixture of copula densities. We develop simulations scenarios to compare the performance of the copula based classifier with classical normal distribution based models, the logistic regression based model and the Independent model. We also apply the techniques to real data, and present the misclassification errors.

DOI

10.25777/82tv-y953

ISBN

9781339126852

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