{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71259"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71259","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Limit Theorems for Processes and Stopping Rules in Adaptive Sequential Estimation","abstract":"This thesis deals with the asymptotic behavior of stopping rules ${\\rm T\\sb{A}}$ and ${\\rm T\\sb{d}}$ proposed by Martinsek (Ann. Statist., 12 (1984):533-550). The asymptotic normality of these stopping rules, when A tends to infinity and d tends to zero respectively, is proved. In the course of proving this, results about the limiting distribution of a closely related stochastic process and of ${\\rm n\\sp{1/2}\\lbrack S\\sbsp{n}{2}(\\\\alpha\\sb{n}})-\\sigma\\sp2(\\alpha\\*)$) are derived. These results are of independent interest.","abstract_html":"This thesis deals with the asymptotic behavior of stopping rules ${\\rm T\\sb{A}}$ and ${\\rm T\\sb{d}}$ proposed by Martinsek (Ann. Statist., 12 (1984):533-550). The asymptotic normality of these stopping rules, when A tends to infinity and d tends to zero respectively, is proved. In the course of proving this, results about the limiting distribution of a closely related stochastic process and of <span class=\"etd-inline-math\">{\\rm n\\sp{1/2}\\lbrack S\\sbsp{n}{2}(\\&alpha;\\sb{n}})-&sigma;\\sp2(&alpha;\\*)</span>) are derived. These results are of independent interest.","abstract_has_math":true,"creators":["Shu, Wun-Yi"],"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":"2014-12-16T06:18:20Z","date_published":"2014-12-16T06:18:20Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Statistics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8721760"],"render_values":[{"text":"(UMI)AAI8721760","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71259","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Shu, Wun-Yi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:20Z","10000-01-01","1987"]},{"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/2142/71259","(UMI)AAI8721760"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis deals with the asymptotic behavior of stopping rules ${\\rm T\\sb{A}}$ and ${\\rm T\\sb{d}}$ proposed by Martinsek (Ann. Statist., 12 (1984):533-550). The asymptotic normality of these stopping rules, when A tends to infinity and d tends to zero respectively, is proved. In the course of proving this, results about the limiting distribution of a closely related stochastic process and of ${\\rm n\\sp{1/2}\\lbrack S\\sbsp{n}{2}(\\\\alpha\\sb{n}})-\\sigma\\sp2(\\alpha\\*)$) are derived. These results are of independent interest.","Made available in DSpace on 2014-12-16T06:18:20Z (GMT). No. of bitstreams: 1 8721760.pdf: 2383663 bytes, checksum: 1f554e8526432b484b8c0dd2ad7a427f (MD5) Previous issue date: 1987","Embargo set by: Seth Robbins for item 71425 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","92 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987."]},{"key":"dc:title","label":"Title","values":["Limit Theorems for Processes and Stopping Rules in Adaptive Sequential Estimation"]}]}],"canonical_facts":{"dc:creator":["Shu, Wun-Yi"],"dc:date":["2014-12-16T06:18:20Z","10000-01-01","1987"],"dc:description":["This thesis deals with the asymptotic behavior of stopping rules ${\\rm T\\sb{A}}$ and ${\\rm T\\sb{d}}$ proposed by Martinsek (Ann. Statist., 12 (1984):533-550). The asymptotic normality of these stopping rules, when A tends to infinity and d tends to zero respectively, is proved. In the course of proving this, results about the limiting distribution of a closely related stochastic process and of ${\\rm n\\sp{1/2}\\lbrack S\\sbsp{n}{2}(\\\\alpha\\sb{n}})-\\sigma\\sp2(\\alpha\\*)$) are derived. These results are of independent interest.","Made available in DSpace on 2014-12-16T06:18:20Z (GMT). No. of bitstreams: 1 8721760.pdf: 2383663 bytes, checksum: 1f554e8526432b484b8c0dd2ad7a427f (MD5) Previous issue date: 1987","Embargo set by: Seth Robbins for item 71425 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","92 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987."],"dc:identifier":["http://hdl.handle.net/2142/71259","(UMI)AAI8721760"],"dc:subject":["Statistics"],"dc:title":["Limit Theorems for Processes and Stopping Rules in Adaptive Sequential Estimation"],"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"}