Date of Award

Winter 1997

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

Dayanand N. Naik

Committee Member

Richardean Bejamin-Coleman

Committee Member

Larry D. Lee

Committee Member

Edward Markowski

Committee Member

John P. Morgan

Abstract

Circular covariance is important in modelling phenomena in epidemiological, communications and numerous physical contexts. We introduce and develop a variety of methods which make it a more versatile tool. First, we present two classes of estimators for use in the presence of missing observations. Using simulations, we show that the mean squared errors of the estimators of one of these classes are smaller than those of the Maximum Likelihood (ML) estimators under certain conditions. Next, we propose and discuss a parsimonious, autoregressive type of circular covariance structure which involves only two parameters. We specify ML and other types of estimators of these parameters, and present techniques for selection between various covariance structures related to circular covariance. Finally, we consider estimation assuming that observations on different individuals are correlated in various ways. This model is generalized for use when varying numbers of observations are taken on individuals. In all these contexts, we combine the measurements on individuals with covariates of varying dimensions, and consider estimation of the correlation between the observations and the covariates.

DOI

10.25777/kev6-4062

ISBN

9780591623345

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