Comparison of ridge and other shrinkage estimation techniques

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dc.contributor.advisorThiart, Christienen_ZA
dc.contributor.authorVumbukani, Bokang Cen_ZA
dc.date.accessioned2014-07-30T17:43:34Z
dc.date.available2014-07-30T17:43:34Z
dc.date.issued2006en_ZA
dc.descriptionIncludes bibliographical references.
dc.description.abstractShrinkage estimation is an increasingly popular class of biased parameter estimation techniques, vital when the columns of the matrix of independent variables X exhibit dependencies or near dependencies. These dependencies often lead to serious problems in least squares estimation: inflated variances and mean squared errors of estimates unstable coefficients, imprecision and improper estimation. Shrinkage methods allow for a little bias and at the same time introduce smaller mean squared error and variances for the biased estimators, compared to those of unbiased estimators. However, shrinkage methods are based on the shrinkage factor, of which estimation depends on the unknown values, often computed from the OLS solution. We argue that the instability of OLS estimates may have an adverse effect on performance of shrinkage estimators. Hence a new method for estimating the shrinkage factors is proposed and applied on ridge and generalized ridge regression. We propose that the new shrinkage factors should be based on the principal components instead of the unstable OLS estimates.en_ZA
dc.identifier.apacitationVumbukani, B. C. (2006). <i>Comparison of ridge and other shrinkage estimation techniques</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Statistical Sciences. Retrieved from http://hdl.handle.net/11427/4364en_ZA
dc.identifier.chicagocitationVumbukani, Bokang C. <i>"Comparison of ridge and other shrinkage estimation techniques."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Statistical Sciences, 2006. http://hdl.handle.net/11427/4364en_ZA
dc.identifier.citationVumbukani, B. 2006. Comparison of ridge and other shrinkage estimation techniques. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Vumbukani, Bokang C AB - Shrinkage estimation is an increasingly popular class of biased parameter estimation techniques, vital when the columns of the matrix of independent variables X exhibit dependencies or near dependencies. These dependencies often lead to serious problems in least squares estimation: inflated variances and mean squared errors of estimates unstable coefficients, imprecision and improper estimation. Shrinkage methods allow for a little bias and at the same time introduce smaller mean squared error and variances for the biased estimators, compared to those of unbiased estimators. However, shrinkage methods are based on the shrinkage factor, of which estimation depends on the unknown values, often computed from the OLS solution. We argue that the instability of OLS estimates may have an adverse effect on performance of shrinkage estimators. Hence a new method for estimating the shrinkage factors is proposed and applied on ridge and generalized ridge regression. We propose that the new shrinkage factors should be based on the principal components instead of the unstable OLS estimates. DA - 2006 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2006 T1 - Comparison of ridge and other shrinkage estimation techniques TI - Comparison of ridge and other shrinkage estimation techniques UR - http://hdl.handle.net/11427/4364 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/4364
dc.identifier.vancouvercitationVumbukani BC. Comparison of ridge and other shrinkage estimation techniques. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Statistical Sciences, 2006 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/4364en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Statistical Sciencesen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherStatistical Sciencesen_ZA
dc.titleComparison of ridge and other shrinkage estimation techniquesen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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