{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/70766"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/70766","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Improved Estimators Under Squared Error Loss (Stein Estimator, Decision Theory, Empirical Bayes, Quadratic, Robust Estimation)","abstract":"Much work on the James-Stein (1964) estimator or an improved estimator under squared error loss has been done with the assumption of independently identically distributed normal errors.","abstract_html":"Much work on the James-Stein (1964) estimator or an improved estimator under squared error loss has been done with the assumption of independently identically distributed normal errors.","abstract_has_math":false,"creators":["Miyazaki, Shigetaka"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Economics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T04:05:09Z","date_published":"2014-12-16T04:05:09Z","updated_at":"2026-07-22T22:26:03Z","subjects":["Statistics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8600268"],"render_values":[{"text":"(UMI)AAI8600268","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/70766","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Miyazaki, Shigetaka"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T04:05:09Z","10000-01-01","1985"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Economics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Statistics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/70766","(UMI)AAI8600268"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Much work on the James-Stein (1964) estimator or an improved estimator under squared error loss has been done with the assumption of independently identically distributed normal errors.","In this thesis behavior of the Stein-type estimators is examined in a regression model under the assumptions of heteroscedasticity and non-normality. Also presented are relationship between the Bayes and the Stein-type estimators, improved estimators under inequality prior restrictions, impacts of pre-testing null hypotheses in estimating parameters, and compromise estimators between the minimum maximum component risk and the minimum ensemble risk. Monte Carlo experiments are done as well as theoretical work on these improved estimators. It is then shown that even under the assumptions of heteroscedasticity and non-normality the Stein-type estimators are still risk superior to the maximum likelihood estimator and conventional robust estimators everywhere on the parameter space. Also, the adaptive Stein estimator introduced by Dey-Berger (1983, JASA) is shown to be risk superior to the conventional Stein estimator under some circumstances.","Made available in DSpace on 2014-12-16T04:05:09Z (GMT). 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Also presented are relationship between the Bayes and the Stein-type estimators, improved estimators under inequality prior restrictions, impacts of pre-testing null hypotheses in estimating parameters, and compromise estimators between the minimum maximum component risk and the minimum ensemble risk. Monte Carlo experiments are done as well as theoretical work on these improved estimators. It is then shown that even under the assumptions of heteroscedasticity and non-normality the Stein-type estimators are still risk superior to the maximum likelihood estimator and conventional robust estimators everywhere on the parameter space. Also, the adaptive Stein estimator introduced by Dey-Berger (1983, JASA) is shown to be risk superior to the conventional Stein estimator under some circumstances.","Made available in DSpace on 2014-12-16T04:05:09Z (GMT). No. of bitstreams: 1 8600268.pdf: 6331623 bytes, checksum: 2ce6090d69b9053b88424143a965b41f (MD5) Previous issue date: 1985","Embargo set by: Seth Robbins for item 70932 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","253 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985."],"dc:identifier":["http://hdl.handle.net/2142/70766","(UMI)AAI8600268"],"dc:subject":["Statistics"],"dc:title":["Improved Estimators Under Squared Error Loss (Stein Estimator, Decision Theory, Empirical Bayes, Quadratic, Robust Estimation)"],"dc:type":["text"],"thesis:degree_discipline":["Economics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:03Z"}