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dc.contributor.advisorWang, Haonan
dc.contributor.advisorMeyer, Mary C.
dc.contributor.authorKim, Soo Young
dc.contributor.committeememberFosdick, Bailey K.
dc.contributor.committeememberOpsomer, Jean D.
dc.contributor.committeememberLuo, J. Rockey
dc.date.accessioned2019-01-07T17:19:10Z
dc.date.available2019-01-07T17:19:10Z
dc.date.issued2018
dc.description2018 Fall.
dc.descriptionIncludes bibliographical references.
dc.description.abstractThe problems associated with heteroskedasticity often lead to incorrect inferences in a regression model, especially when the form of the heteroskedasticity is obscure. In this dissertation, I present methods to estimate a variance function in a heteroskedastic regression model where the variance function is assumed to be smooth and monotone in a predictor variable. Maximum likelihood estimation of the variance function is derived under normal or double-exponential error distribution assumptions based on regression splines and the cone projection algorithm. A penalized spline estimator is also introduced, and the estimator performs well when there exists a spiking problem at a boundary of domain. The convergence rates of the estimated variance functions are derived, and simulations show that it tends to be closer to the true variance function in a variety of scenarios compared to the existing method. The estimated variance functions from the proposed methods provide improved inference about the mean function, in terms of a coverage probability and an average length for an interval estimate. The utility of the method is illustrated through the analysis of real datasets such as LIDAR data, abalone data, California air pollution data, and U.S. temperature data. The methodology is implemented in the R package cgam. In addition to the variance function estimation method, the hypothesis test procedure of a smooth and monotone variance function is discussed. The likelihood ratio test is introduced under normal or double-exponential error distribution assumptions. Comparisons of the proposed test with existing tests are conducted through simulations.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierKim_colostate_0053A_15131.pdf
dc.identifier.urihttps://hdl.handle.net/10217/193107
dc.languageEnglish
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019 - CSU Theses and Dissertations
dc.rightsCopyright of the original work is retained by the author.
dc.subjectconvergence rate
dc.subjectcone projection
dc.subjectregression splines
dc.titleImproved inference in heteroskedastic regression models with monotone variance function estimation
dc.typeText
dcterms.rights.dplaThe copyright and related rights status of this item has not been evaluated (https://rightsstatements.org/vocab/CNE/1.0/). Please refer to the organization that has made the Item available for more information.
thesis.degree.disciplineStatistics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)


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