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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Hartley, Andrew Montgomery"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Dayanand N. Naik","Richardean Bejamin-Coleman","Larry D. Lee","Edward Markowski","John P. Morgan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1997,"date_issued":"1997-01-01T08:00:00Z","date_published":"1997-01-01T08:00:00Z","updated_at":"2026-07-24T03:34:53Z","subjects":["Covariance structures","Familial data","Applied Statistics","Mathematics"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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"]},{"key":"dc:title","label":"Title","values":["Analysis of Repeated Measures Data Under Circular Covariance"]}]}],"canonical_facts":{"dc:contributor":["Dayanand N. Naik","Richardean Bejamin-Coleman","Larry D. Lee","Edward Markowski","John P. Morgan"],"dc:creator":["Hartley, Andrew Montgomery"],"dc:date.available":["2019-06-05T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["9780591623345","https://digitalcommons.odu.edu/mathstat_etds/14"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Covariance structures","Familial data","Applied Statistics","Mathematics"],"dc:title":["Analysis of Repeated Measures Data Under Circular Covariance"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:34:53Z"}