{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71502"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71502","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 Beta-Protection in the Presence of Nuisance Parameters","abstract":"In this thesis we study sequential procedures for constructing one-sided and bounded sequential confidence sets with $\\beta$-protection and coverage probability at least 1 $-$ $\\alpha$ for the mean of a distribution in the presence of nuisance parameters.","abstract_html":"In this thesis we study sequential procedures for constructing one-sided and bounded sequential confidence sets with <span class=\"etd-inline-math\">&beta;</span>-protection and coverage probability at least 1 $-$ <span class=\"etd-inline-math\">&alpha;</span> for the mean of a distribution in the presence of nuisance parameters.","abstract_has_math":true,"creators":["Kim, Sung Lai"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["Wijsman, Robert A.,"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T18:31:32Z","date_published":"2014-12-16T18:31:32Z","updated_at":"2026-07-22T22:26:05Z","subjects":["Statistics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8803088"],"render_values":[{"text":"(UMI)AAI8803088","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71502","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Wijsman, Robert A.,"]},{"key":"dc:creator","label":"Author","values":["Kim, Sung Lai"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T18:31:32Z","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/2142/71502","(UMI)AAI8803088"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we study sequential procedures for constructing one-sided and bounded sequential confidence sets with $\\beta$-protection and coverage probability at least 1 $-$ $\\alpha$ for the mean of a distribution in the presence of nuisance parameters.","Let $\\{X\\sb{n}$: n = 1,2, dots,$\\}$ be i i d p-variate (p $\\geq$ 1) random variables with distribution $P\\sb{\\theta}$, $\\theta\\in\\Theta$. The parameter space $\\Theta$ is some abstract set for which various choices will be made. The mean $\\mu$ = $\\mu(\\theta)$ of $P\\sb{\\theta}$ is the parameter of interest, the rest of $\\theta$ will be regarded as a nuisance parameter. In the simplest case $\\mu$ is real valued and there is given an imprecision function $\\delta(\\mu)$ $&gt;$ 0 and error probabilities 0 $$ 1). In the univariate case several asymptotic properties of the stopping time are obtained in various limiting situations.","Made available in DSpace on 2014-12-16T18:31:32Z (GMT). No. of bitstreams: 1 8803088.pdf: 1869532 bytes, checksum: 3a718d24933413ff0c3ca92255d566bb (MD5) Previous issue date: 1987","Embargo set by: Seth Robbins for item 71668 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","56 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987."]},{"key":"dc:title","label":"Title","values":["Sequential Confidence Sets With Beta-Protection in the Presence of Nuisance Parameters"]}]}],"canonical_facts":{"dc:contributor":["Wijsman, Robert A.,"],"dc:creator":["Kim, Sung Lai"],"dc:date":["2014-12-16T18:31:32Z","10000-01-01","1987"],"dc:description":["In this thesis we study sequential procedures for constructing one-sided and bounded sequential confidence sets with $\\beta$-protection and coverage probability at least 1 $-$ $\\alpha$ for the mean of a distribution in the presence of nuisance parameters.","Let $\\{X\\sb{n}$: n = 1,2, dots,$\\}$ be i i d p-variate (p $\\geq$ 1) random variables with distribution $P\\sb{\\theta}$, $\\theta\\in\\Theta$. The parameter space $\\Theta$ is some abstract set for which various choices will be made. The mean $\\mu$ = $\\mu(\\theta)$ of $P\\sb{\\theta}$ is the parameter of interest, the rest of $\\theta$ will be regarded as a nuisance parameter. In the simplest case $\\mu$ is real valued and there is given an imprecision function $\\delta(\\mu)$ $&gt;$ 0 and error probabilities 0 $$ 1). In the univariate case several asymptotic properties of the stopping time are obtained in various limiting situations.","Made available in DSpace on 2014-12-16T18:31:32Z (GMT). No. of bitstreams: 1 8803088.pdf: 1869532 bytes, checksum: 3a718d24933413ff0c3ca92255d566bb (MD5) Previous issue date: 1987","Embargo set by: Seth Robbins for item 71668 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","56 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987."],"dc:identifier":["http://hdl.handle.net/2142/71502","(UMI)AAI8803088"],"dc:subject":["Statistics"],"dc:title":["Sequential Confidence Sets With Beta-Protection in the Presence of Nuisance Parameters"],"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"}