{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71202"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71202","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Optimal Simultaneous Confidence Bounds in Regression","abstract":"The problem of finding optimal simultaneous confidence bounds for multilinear regression functions with intercept, over bounded regions, is considered. Conditions are derived which imply that the Scheffe-type bound beats the constant width bound for the case of one-sided or two-sided bounding, in the sense of having smaller average width with respect to Lebesgue measure over the region, when coverage probabilities are equated. These conditions are shown to hold for many important regression designs. A new class of bounds for which the coverage probability may be easily computed is introduced. Using this class, the Scheffe-type bound is shown to be suboptimal, for some situations. This is in contrast to a result of Bohrer (1973) which gives the optimality of Scheffe-type bounds for the non-intercept case. The notion of a simultaneous confidence bound is redefined by replacing coverage probability by expected coverage measure. Under fairly general conditions bounds can be derived which minimize a functional of the width subject to a lower bound on the expected coverage measure.","abstract_html":"The problem of finding optimal simultaneous confidence bounds for multilinear regression functions with intercept, over bounded regions, is considered. Conditions are derived which imply that the Scheffe-type bound beats the constant width bound for the case of one-sided or two-sided bounding, in the sense of having smaller average width with respect to Lebesgue measure over the region, when coverage probabilities are equated. These conditions are shown to hold for many important regression designs. A new class of bounds for which the coverage probability may be easily computed is introduced. Using this class, the Scheffe-type bound is shown to be suboptimal, for some situations. This is in contrast to a result of Bohrer (1973) which gives the optimality of Scheffe-type bounds for the non-intercept case. The notion of a simultaneous confidence bound is redefined by replacing coverage probability by expected coverage measure. Under fairly general conditions bounds can be derived which minimize a functional of the width subject to a lower bound on the expected coverage measure.","abstract_has_math":false,"creators":["Naiman, Daniel Quitt"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T06:18:02Z","date_published":"2014-12-16T06:18:02Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8218529"],"render_values":[{"text":"(UMI)AAI8218529","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71202","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Naiman, Daniel Quitt"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:02Z","10000-01-01","1982"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"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":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71202","(UMI)AAI8218529"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The problem of finding optimal simultaneous confidence bounds for multilinear regression functions with intercept, over bounded regions, is considered. Conditions are derived which imply that the Scheffe-type bound beats the constant width bound for the case of one-sided or two-sided bounding, in the sense of having smaller average width with respect to Lebesgue measure over the region, when coverage probabilities are equated. These conditions are shown to hold for many important regression designs. A new class of bounds for which the coverage probability may be easily computed is introduced. Using this class, the Scheffe-type bound is shown to be suboptimal, for some situations. This is in contrast to a result of Bohrer (1973) which gives the optimality of Scheffe-type bounds for the non-intercept case. The notion of a simultaneous confidence bound is redefined by replacing coverage probability by expected coverage measure. Under fairly general conditions bounds can be derived which minimize a functional of the width subject to a lower bound on the expected coverage measure.","Made available in DSpace on 2014-12-16T06:18:02Z (GMT). No. of bitstreams: 1 8218529.pdf: 3319234 bytes, checksum: a0b5f0270c464d74ae4e5a5c6a98e469 (MD5) Previous issue date: 1982","Embargo set by: Seth Robbins for item 71368 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","154 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1982."]},{"key":"dc:title","label":"Title","values":["Optimal Simultaneous Confidence Bounds in Regression"]}]}],"canonical_facts":{"dc:creator":["Naiman, Daniel Quitt"],"dc:date":["2014-12-16T06:18:02Z","10000-01-01","1982"],"dc:description":["The problem of finding optimal simultaneous confidence bounds for multilinear regression functions with intercept, over bounded regions, is considered. Conditions are derived which imply that the Scheffe-type bound beats the constant width bound for the case of one-sided or two-sided bounding, in the sense of having smaller average width with respect to Lebesgue measure over the region, when coverage probabilities are equated. These conditions are shown to hold for many important regression designs. A new class of bounds for which the coverage probability may be easily computed is introduced. Using this class, the Scheffe-type bound is shown to be suboptimal, for some situations. This is in contrast to a result of Bohrer (1973) which gives the optimality of Scheffe-type bounds for the non-intercept case. The notion of a simultaneous confidence bound is redefined by replacing coverage probability by expected coverage measure. Under fairly general conditions bounds can be derived which minimize a functional of the width subject to a lower bound on the expected coverage measure.","Made available in DSpace on 2014-12-16T06:18:02Z (GMT). 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