{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/21596"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/21596","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Comparison of several curves in the context of nonparametric regression","abstract":"Consider the model $y\\sb{lj} = \\mu\\sb{l}(t\\sb{j})$ + $\\varepsilon\\sb{lj}$, $l = 1,..,m$ and $j = 1,..,n,$ where $\\varepsilon\\sb{lj}$ are independent mean zero finite variance random variables. Under the above setting we test the hypotheses","abstract_html":"Consider the model <span class=\"etd-inline-math\">y\\sb{lj} = &mu;\\sb{l}(t\\sb{j})</span> + $\\varepsilon\\sb{lj}$, $l = 1,..,m$ and $j = 1,..,n,$ where $\\varepsilon\\sb{lj}$ are independent mean zero finite variance random variables. Under the above setting we test the hypotheses","abstract_has_math":true,"creators":["Amarasinghe, Upali Ananda"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["Cox, Dennis D."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:13:22Z","date_published":"2011-05-07T13:13:22Z","updated_at":"2026-07-22T22:25:18Z","subjects":["Statistics"],"languages":["eng"],"rights":["Copyright 1991 Amarasinghe, Upali Ananda"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9210725","(UMI)AAI9210725"],"render_values":[{"text":"AAI9210725","href":null,"code":true},{"text":"(UMI)AAI9210725","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/21596","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Cox, Dennis D."]},{"key":"dc:creator","label":"Author","values":["Amarasinghe, Upali Ananda"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:13:22Z","10000-01-01","1991"]},{"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":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1991 Amarasinghe, Upali Ananda"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9210725","(UMI)AAI9210725","http://hdl.handle.net/2142/21596"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Consider the model $y\\sb{lj} = \\mu\\sb{l}(t\\sb{j})$ + $\\varepsilon\\sb{lj}$, $l = 1,..,m$ and $j = 1,..,n,$ where $\\varepsilon\\sb{lj}$ are independent mean zero finite variance random variables. Under the above setting we test the hypotheses","$H\\sb0 : \\mu\\sb1 (t) {=..=}\\ \\mu\\sb{m}(t)$ vs $H\\sb{a} : \\mu\\sb{l}(t)$ are not all equal.","Different procedures for testing the above hypotheses are studied. Test procedures are based on comparing estimates of the regression functions. Both smoothing spline and orthogonal series estimators are considered and the smoothing parameters are selected using Generalized Cross Validation criterion. Under some regularity conditions the asymptotic distributions of some of the test statistics are shown to be normal. Asymptotic power comparisons for the shift alternative are discussed. Comparison of regression curves in Bayesian nonparametric regression is also investigated.","Made available in DSpace on 2011-05-07T13:13:22Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9210725.pdf: 4962173 bytes, checksum: c252adc48055c3b0afa61915265a01b9 (MD5) Previous issue date: 1991","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:51:51Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:23:51-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Comparison of several curves in the context of nonparametric regression"]}]}],"canonical_facts":{"dc:contributor":["Cox, Dennis D."],"dc:creator":["Amarasinghe, Upali Ananda"],"dc:date":["2011-05-07T13:13:22Z","10000-01-01","1991"],"dc:description":["Consider the model $y\\sb{lj} = \\mu\\sb{l}(t\\sb{j})$ + $\\varepsilon\\sb{lj}$, $l = 1,..,m$ and $j = 1,..,n,$ where $\\varepsilon\\sb{lj}$ are independent mean zero finite variance random variables. Under the above setting we test the hypotheses","$H\\sb0 : \\mu\\sb1 (t) {=..=}\\ \\mu\\sb{m}(t)$ vs $H\\sb{a} : \\mu\\sb{l}(t)$ are not all equal.","Different procedures for testing the above hypotheses are studied. Test procedures are based on comparing estimates of the regression functions. Both smoothing spline and orthogonal series estimators are considered and the smoothing parameters are selected using Generalized Cross Validation criterion. Under some regularity conditions the asymptotic distributions of some of the test statistics are shown to be normal. Asymptotic power comparisons for the shift alternative are discussed. Comparison of regression curves in Bayesian nonparametric regression is also investigated.","Made available in DSpace on 2011-05-07T13:13:22Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9210725.pdf: 4962173 bytes, checksum: c252adc48055c3b0afa61915265a01b9 (MD5) Previous issue date: 1991","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:51:51Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:23:51-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9210725","(UMI)AAI9210725","http://hdl.handle.net/2142/21596"],"dc:language":["eng"],"dc:rights":["Copyright 1991 Amarasinghe, Upali Ananda"],"dc:subject":["Statistics"],"dc:title":["Comparison of several curves in the context of nonparametric regression"],"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":"2026-07-22T22:25:18Z"}