{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/4364"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/4364","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Comparison of ridge and other shrinkage estimation techniques","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Vumbukani, Bokang C"],"institution":"Department of Statistical Sciences","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Thiart, Christien"],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006","date_published":"2006","updated_at":"2026-07-22T22:22:39Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/4364","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Thiart, Christien"]},{"key":"dc:creator","label":"Author","values":["Vumbukani, Bokang C"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-07-30T17:43:34Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-07-30T17:43:34Z"]},{"key":"dc:date.issued","label":"Date","values":["2006"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Statistical Sciences"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/4364"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes bibliographical references."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Comparison of ridge and other shrinkage estimation techniques"]}]}],"canonical_facts":{"dc:contributor.advisor":["Thiart, Christien"],"dc:creator":["Vumbukani, Bokang C"],"dc:date.accessioned":["2014-07-30T17:43:34Z"],"dc:date.available":["2014-07-30T17:43:34Z"],"dc:date.issued":["2006"],"dc:description":["Includes bibliographical references."],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/11427/4364"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Statistical Sciences"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Comparison of ridge and other shrinkage estimation techniques"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:22:39Z"}