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Estimation and linear prediction for regression, autoregression and ARMA with infinite variance data

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dc.contributor.authorCline, Daren B. H., author
dc.contributor.authorResnick, Sidney I., advisor
dc.contributor.authorBrockwell, Peter J., advisor
dc.contributor.authorLocker, John, committee member
dc.contributor.authorDavis, Richard A., committee member
dc.contributor.authorBoes, Duane C., committee member
dc.date.accessioned2016-09-09T21:53:27Z
dc.date.available2016-09-09T21:53:27Z
dc.date.issued1983
dc.descriptionIncludes bibliographical references (pages 127-128).
dc.description.abstractThis dissertation is divided into four parts, each of which considers random variables from distributions with regularly varying tails and/or in a stable domain of attraction. Part I considers the existence of infinite series of an independent sequence of such random variables and the relationship of the probability of large values of the series to the probability of large values of the first component. Part II applies Part I in order to provide a linear predictor for ARMA time series (again with regularly varying tails). This predictor is designed to minimize the probability of large prediction errors relative to the tails of the noise distribution. Part III investigates the products of independent random variables where one has distribution in a stable domain of attraction and gives conditions for which the product distribution is in a stable domain of attraction. Part IV considers estimation of the regression parameter in a model where the independent variables are in a stable domain of attraction. Consistency for certain M-estimators is proved. Utilizing portions of Part III this final part gives necessary and sufficient conditions for consistency of least squares estimators and provides the asymptotic distribution of least squares estimators.
dc.format.mediumdoctoral dissertations
dc.identifier.urihttp://hdl.handle.net/10217/177235
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relationCatalog record number (MMS ID): 991004790059703361
dc.relationQA273.C65 1983
dc.relation.ispartof1980-1999
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subject.lcshRandom variables
dc.subject.lcshPrediction theory
dc.titleEstimation and linear prediction for regression, autoregression and ARMA with infinite variance data
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). 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).
thesis.degree.disciplineStatistics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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