{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19451"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19451","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Optimal bandwidth selection rule for kernel regression estimator with dependent variables","abstract":"Let $\\{$(X$\\sb{\\rm t}$,Y$\\sb{\\rm t}$): t $\\in$ N$\\}$ be a strictly stationary process with X$\\sb{\\rm t}$ being R$\\sp{\\rm d}$-valued and Y$\\sb{\\rm t}$ being real valued. Consider the problem of estimating the conditional expectation function, m(x) = E(Y$\\sb{\\rm t}\\vert$ X$\\sb{\\rm t}$ = x), using (X$\\sb1,$Y$\\sb1$),$\\...$ (X$\\sb{\\rm n}$,Y$\\sb{\\rm n}$). (For example, suppose Z$\\sb{\\rm t}$, t = 0, $\\pm$1, $\\pm$2,.. is a real valued stationary time series and p is a positive integer. Set X$\\sb{\\rm t}$ = (Z$\\sb{\\rm t+1},\\...$,Z$\\sb{\\rm t+d}$) and Y$\\sb{\\rm t}$ = Z$\\sb{\\rm t+d+p}$. Then (X$\\sb{\\rm t}$,Y$\\sb{\\rm t}$), t = 0, $\\pm$1,.. is a stationary time series and m(x) = E(Z$\\sb{\\rm d+p}\\vert$Z$\\sb1,\\...$Z$\\sb{\\rm d}$).) We consider kernel estimators of m(x). Recently, convergence properties of the kernel estimator have been developed under certain dependence structures for the process (X$\\sb{\\rm t}$,Y$\\sb{\\rm t}$). One of the crucial points in applying a kernel estimator is the choice of bandwidth. The main purpose of this work is to establish asymptotic optimality for a bandwidth selection rule under dependence which can be interpreted in terms of cross validation. In addition, some moment bounds for dependent variables will be established, which give more flexible bounds than existing ones.","abstract_html":"Let $\\{$(X$\\sb{\\rm t}$,Y$\\sb{\\rm t}$): t $\\in$ N$\\}$ be a strictly stationary process with X$\\sb{\\rm t}$ being R$\\sp{\\rm d}$-valued and Y$\\sb{\\rm t}$ being real valued. Consider the problem of estimating the conditional expectation function, m(x) = E(Y$\\sb{\\rm t}\\vert$ X$\\sb{\\rm t}$ = x), using (X$\\sb1,$Y$\\sb1$),$\\...$ (X$\\sb{\\rm n}$,Y$\\sb{\\rm n}$). (For example, suppose Z$\\sb{\\rm t}$, t = 0, $\\pm$1, $\\pm$2,.. is a real valued stationary time series and p is a positive integer. Set X$\\sb{\\rm t}$ = (Z$\\sb{\\rm t+1},\\...$,Z$\\sb{\\rm t+d}$) and Y$\\sb{\\rm t}$ = Z$\\sb{\\rm t+d+p}$. Then (X$\\sb{\\rm t}$,Y$\\sb{\\rm t}$), t = 0, $\\pm$1,.. is a stationary time series and m(x) = E(Z$\\sb{\\rm d+p}\\vert$Z$\\sb1,\\...$Z$\\sb{\\rm d}$).) We consider kernel estimators of m(x). Recently, convergence properties of the kernel estimator have been developed under certain dependence structures for the process (X$\\sb{\\rm t}$,Y$\\sb{\\rm t}$). One of the crucial points in applying a kernel estimator is the choice of bandwidth. The main purpose of this work is to establish asymptotic optimality for a bandwidth selection rule under dependence which can be interpreted in terms of cross validation. In addition, some moment bounds for dependent variables will be established, which give more flexible bounds than existing ones.","abstract_has_math":true,"creators":["Kim, Tae Yoon"],"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":"2011-05-07T12:07:59Z","date_published":"2011-05-07T12:07:59Z","updated_at":"2026-07-22T22:25:14Z","subjects":["Statistics"],"languages":["eng"],"rights":["Copyright 1990 Kim, Tae Yoon"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9026227","(UMI)AAI9026227"],"render_values":[{"text":"AAI9026227","href":null,"code":true},{"text":"(UMI)AAI9026227","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19451","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":["Kim, Tae Yoon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:07:59Z","10000-01-01","1990"]},{"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 1990 Kim, Tae Yoon"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9026227","(UMI)AAI9026227","http://hdl.handle.net/2142/19451"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Let $\\{$(X$\\sb{\\rm t}$,Y$\\sb{\\rm t}$): t $\\in$ N$\\}$ be a strictly stationary process with X$\\sb{\\rm t}$ being R$\\sp{\\rm d}$-valued and Y$\\sb{\\rm t}$ being real valued. Consider the problem of estimating the conditional expectation function, m(x) = E(Y$\\sb{\\rm t}\\vert$ X$\\sb{\\rm t}$ = x), using (X$\\sb1,$Y$\\sb1$),$\\...$ (X$\\sb{\\rm n}$,Y$\\sb{\\rm n}$). (For example, suppose Z$\\sb{\\rm t}$, t = 0, $\\pm$1, $\\pm$2,.. is a real valued stationary time series and p is a positive integer. Set X$\\sb{\\rm t}$ = (Z$\\sb{\\rm t+1},\\...$,Z$\\sb{\\rm t+d}$) and Y$\\sb{\\rm t}$ = Z$\\sb{\\rm t+d+p}$. Then (X$\\sb{\\rm t}$,Y$\\sb{\\rm t}$), t = 0, $\\pm$1,.. is a stationary time series and m(x) = E(Z$\\sb{\\rm d+p}\\vert$Z$\\sb1,\\...$Z$\\sb{\\rm d}$).) We consider kernel estimators of m(x). Recently, convergence properties of the kernel estimator have been developed under certain dependence structures for the process (X$\\sb{\\rm t}$,Y$\\sb{\\rm t}$). One of the crucial points in applying a kernel estimator is the choice of bandwidth. The main purpose of this work is to establish asymptotic optimality for a bandwidth selection rule under dependence which can be interpreted in terms of cross validation. In addition, some moment bounds for dependent variables will be established, which give more flexible bounds than existing ones.","Made available in DSpace on 2011-05-07T12:07:59Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9026227.pdf: 3125228 bytes, checksum: ad799f8c8fbfb54a4aa2eac179405566 (MD5) Previous issue date: 1990","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:37:03Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:15:10-05:00 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":["Optimal bandwidth selection rule for kernel regression estimator with dependent variables"]}]}],"canonical_facts":{"dc:contributor":["Cox, Dennis D."],"dc:creator":["Kim, Tae Yoon"],"dc:date":["2011-05-07T12:07:59Z","10000-01-01","1990"],"dc:description":["Let $\\{$(X$\\sb{\\rm t}$,Y$\\sb{\\rm t}$): t $\\in$ N$\\}$ be a strictly stationary process with X$\\sb{\\rm t}$ being R$\\sp{\\rm d}$-valued and Y$\\sb{\\rm t}$ being real valued. Consider the problem of estimating the conditional expectation function, m(x) = E(Y$\\sb{\\rm t}\\vert$ X$\\sb{\\rm t}$ = x), using (X$\\sb1,$Y$\\sb1$),$\\...$ (X$\\sb{\\rm n}$,Y$\\sb{\\rm n}$). (For example, suppose Z$\\sb{\\rm t}$, t = 0, $\\pm$1, $\\pm$2,.. is a real valued stationary time series and p is a positive integer. Set X$\\sb{\\rm t}$ = (Z$\\sb{\\rm t+1},\\...$,Z$\\sb{\\rm t+d}$) and Y$\\sb{\\rm t}$ = Z$\\sb{\\rm t+d+p}$. Then (X$\\sb{\\rm t}$,Y$\\sb{\\rm t}$), t = 0, $\\pm$1,.. is a stationary time series and m(x) = E(Z$\\sb{\\rm d+p}\\vert$Z$\\sb1,\\...$Z$\\sb{\\rm d}$).) We consider kernel estimators of m(x). Recently, convergence properties of the kernel estimator have been developed under certain dependence structures for the process (X$\\sb{\\rm t}$,Y$\\sb{\\rm t}$). One of the crucial points in applying a kernel estimator is the choice of bandwidth. The main purpose of this work is to establish asymptotic optimality for a bandwidth selection rule under dependence which can be interpreted in terms of cross validation. In addition, some moment bounds for dependent variables will be established, which give more flexible bounds than existing ones.","Made available in DSpace on 2011-05-07T12:07:59Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9026227.pdf: 3125228 bytes, checksum: ad799f8c8fbfb54a4aa2eac179405566 (MD5) Previous issue date: 1990","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:37:03Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:15:10-05:00 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":["AAI9026227","(UMI)AAI9026227","http://hdl.handle.net/2142/19451"],"dc:language":["eng"],"dc:rights":["Copyright 1990 Kim, Tae Yoon"],"dc:subject":["Statistics"],"dc:title":["Optimal bandwidth selection rule for kernel regression estimator with dependent variables"],"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":"2026-07-22T22:25:14Z"}