{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71501"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71501","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Sequential Confidence Sets With Guaranteed Coverage Probability and Beta-Protection in Multiparameter Families","abstract":"We consider a class of invariant sequential procedures for constructing one-sided and two-sided confidence sets for a parameter $\\gamma$ in R$\\sp{k}$, with the property that they have a coverage probability at least 1 - $\\alpha$ and probability of covering a certain set of false values at most $\\beta$. In addition, a method is proposed that is capable of generating a wide variety of sequential confidence sets (not necessarily equivariant) and some of its properties are investigated. The asymptotic properties of the stopping time are studied and the limiting values of the error probabilities are found as the parameter approaches the boundary points. Applications are made to the problem of simultaneous confidence sets for the mean and variance of a normal random variable and for its multivariate analogue.","abstract_html":"We consider a class of invariant sequential procedures for constructing one-sided and two-sided confidence sets for a parameter <span class=\"etd-inline-math\">&gamma;</span> in R$\\sp{k}$, with the property that they have a coverage probability at least 1 - <span class=\"etd-inline-math\">&alpha;</span> and probability of covering a certain set of false values at most <span class=\"etd-inline-math\">&beta;</span>. In addition, a method is proposed that is capable of generating a wide variety of sequential confidence sets (not necessarily equivariant) and some of its properties are investigated. The asymptotic properties of the stopping time are studied and the limiting values of the error probabilities are found as the parameter approaches the boundary points. Applications are made to the problem of simultaneous confidence sets for the mean and variance of a normal random variable and for its multivariate analogue.","abstract_has_math":true,"creators":["Fakhre-Zakeri, Issa"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["Awijsmon, Robert,"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T18:31:31Z","date_published":"2014-12-16T18:31:31Z","updated_at":"2026-07-22T22:26:05Z","subjects":["Statistics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8803033"],"render_values":[{"text":"(UMI)AAI8803033","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71501","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Awijsmon, Robert,"]},{"key":"dc:creator","label":"Author","values":["Fakhre-Zakeri, Issa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T18:31:31Z","10000-01-01","1987"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Statistics"]},{"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/2142/71501","(UMI)AAI8803033"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We consider a class of invariant sequential procedures for constructing one-sided and two-sided confidence sets for a parameter $\\gamma$ in R$\\sp{k}$, with the property that they have a coverage probability at least 1 - $\\alpha$ and probability of covering a certain set of false values at most $\\beta$. In addition, a method is proposed that is capable of generating a wide variety of sequential confidence sets (not necessarily equivariant) and some of its properties are investigated. The asymptotic properties of the stopping time are studied and the limiting values of the error probabilities are found as the parameter approaches the boundary points. Applications are made to the problem of simultaneous confidence sets for the mean and variance of a normal random variable and for its multivariate analogue.","Made available in DSpace on 2014-12-16T18:31:31Z (GMT). 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In addition, a method is proposed that is capable of generating a wide variety of sequential confidence sets (not necessarily equivariant) and some of its properties are investigated. The asymptotic properties of the stopping time are studied and the limiting values of the error probabilities are found as the parameter approaches the boundary points. Applications are made to the problem of simultaneous confidence sets for the mean and variance of a normal random variable and for its multivariate analogue.","Made available in DSpace on 2014-12-16T18:31:31Z (GMT). No. of bitstreams: 1 8803033.pdf: 1832930 bytes, checksum: 2b1e85e5cf3c2bde837474df5d3db60b (MD5) Previous issue date: 1987","Embargo set by: Seth Robbins for item 71667 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","72 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987."],"dc:identifier":["http://hdl.handle.net/2142/71501","(UMI)AAI8803033"],"dc:subject":["Statistics"],"dc:title":["Sequential Confidence Sets With Guaranteed Coverage Probability and Beta-Protection in Multiparameter Families"],"dc:type":["text"],"thesis:degree_discipline":["Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:05Z"}