{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71231"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71231","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Sequential and Non-Sequential Confidence Intervals With Guaranteed Coverage Probability and Beta-Protection (Estimation, Statistics, Minimaxity)","abstract":"In this thesis we examine several problems related to the construction of one-sided confidence intervals for the mean of a distribution. Let (mu) be the mean (of a normal distribution with variance 1, or of a 1-parameter exponential distribution) and let (phi)((mu)) be a function of (mu). Given error probabilities (alpha) and (beta), we require that the interval I satisfy P(,(mu)) (mu) (ELEM) I (GREATERTHEQ) 1 - (alpha) and P(,(mu)) (phi)((mu)) (ELEM) I (LESSTHEQ) (beta) for all (mu).","abstract_html":"In this thesis we examine several problems related to the construction of one-sided confidence intervals for the mean of a distribution. Let (mu) be the mean (of a normal distribution with variance 1, or of a 1-parameter exponential distribution) and let (phi)((mu)) be a function of (mu). Given error probabilities (alpha) and (beta), we require that the interval I satisfy P(,(mu)) (mu) (ELEM) I (GREATERTHEQ) 1 - (alpha) and P(,(mu)) (phi)((mu)) (ELEM) I (LESSTHEQ) (beta) for all (mu).","abstract_has_math":false,"creators":["Juhlin, Kenton Duane"],"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":"2014-12-16T06:18:12Z","date_published":"2014-12-16T06:18:12Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Statistics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8511624"],"render_values":[{"text":"(UMI)AAI8511624","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71231","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Juhlin, Kenton Duane"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:12Z","10000-01-01","1985"]},{"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":["Statistics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71231","(UMI)AAI8511624"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we examine several problems related to the construction of one-sided confidence intervals for the mean of a distribution. Let (mu) be the mean (of a normal distribution with variance 1, or of a 1-parameter exponential distribution) and let (phi)((mu)) be a function of (mu). Given error probabilities (alpha) and (beta), we require that the interval I satisfy P(,(mu)) (mu) (ELEM) I (GREATERTHEQ) 1 - (alpha) and P(,(mu)) (phi)((mu)) (ELEM) I (LESSTHEQ) (beta) for all (mu).","For some specific problems we study, there are fixed sample size procedures which are solutions. For such procedures we study their minimaxity and admissibility.","If no fixed sample size procedure is a solution, we show the existence of sequential procedures which solve the problem. For some of these we provide numerical results which give some measure of how well the procedures perform. We give details of the computational techniques; these have applicability to sequential problems other than the ones we studied.","Made available in DSpace on 2014-12-16T06:18:12Z (GMT). No. of bitstreams: 1 8511624.pdf: 2981136 bytes, checksum: 4c1e53b9b4b20c340293de8e44e4da21 (MD5) Previous issue date: 1985","Embargo set by: Seth Robbins for item 71397 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","142 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985."]},{"key":"dc:title","label":"Title","values":["Sequential and Non-Sequential Confidence Intervals With Guaranteed Coverage Probability and Beta-Protection (Estimation, Statistics, Minimaxity)"]}]}],"canonical_facts":{"dc:creator":["Juhlin, Kenton Duane"],"dc:date":["2014-12-16T06:18:12Z","10000-01-01","1985"],"dc:description":["In this thesis we examine several problems related to the construction of one-sided confidence intervals for the mean of a distribution. Let (mu) be the mean (of a normal distribution with variance 1, or of a 1-parameter exponential distribution) and let (phi)((mu)) be a function of (mu). Given error probabilities (alpha) and (beta), we require that the interval I satisfy P(,(mu)) (mu) (ELEM) I (GREATERTHEQ) 1 - (alpha) and P(,(mu)) (phi)((mu)) (ELEM) I (LESSTHEQ) (beta) for all (mu).","For some specific problems we study, there are fixed sample size procedures which are solutions. For such procedures we study their minimaxity and admissibility.","If no fixed sample size procedure is a solution, we show the existence of sequential procedures which solve the problem. For some of these we provide numerical results which give some measure of how well the procedures perform. We give details of the computational techniques; these have applicability to sequential problems other than the ones we studied.","Made available in DSpace on 2014-12-16T06:18:12Z (GMT). No. of bitstreams: 1 8511624.pdf: 2981136 bytes, checksum: 4c1e53b9b4b20c340293de8e44e4da21 (MD5) Previous issue date: 1985","Embargo set by: Seth Robbins for item 71397 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","142 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985."],"dc:identifier":["http://hdl.handle.net/2142/71231","(UMI)AAI8511624"],"dc:subject":["Statistics"],"dc:title":["Sequential and Non-Sequential Confidence Intervals With Guaranteed Coverage Probability and Beta-Protection (Estimation, Statistics, Minimaxity)"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:04Z"}