{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/87401"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/87401","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Power Transformation Towards Linear or Partially Linear Quantile Regression Models","abstract":"In this thesis, we consider a family of parametric power transformations for the dependent variable such that a linear or partially linear quantile regression model holds after transformation. The two models being considered are the power-transformed linear quantile regression model and power-transformed partially linear quantile regression model, respectively. We use a cusum process of residuals to measure lack of fit for a given quantile function. A power transformation is chosen to minimize the lack of fit. For the power-transformed linear quantile regression model, we show that the proposed estimator is consistent and asymptotically normal under some mild conditions. We demonstrate that the proposed approach works better than competing methods in the presence of heteroscedasticity and heavy-tails. Inferences about the transformation parameter and about the covariate effects are considered mathematically as well as empirically. A test for the adequacy of the power-transformation models is also proposed. For the power-transformed partially linear quantile regression model, we establish the consistency property for the proposed estimator.","abstract_html":"In this thesis, we consider a family of parametric power transformations for the dependent variable such that a linear or partially linear quantile regression model holds after transformation. The two models being considered are the power-transformed linear quantile regression model and power-transformed partially linear quantile regression model, respectively. We use a cusum process of residuals to measure lack of fit for a given quantile function. A power transformation is chosen to minimize the lack of fit. For the power-transformed linear quantile regression model, we show that the proposed estimator is consistent and asymptotically normal under some mild conditions. We demonstrate that the proposed approach works better than competing methods in the presence of heteroscedasticity and heavy-tails. Inferences about the transformation parameter and about the covariate effects are considered mathematically as well as empirically. A test for the adequacy of the power-transformation models is also proposed. For the power-transformed partially linear quantile regression model, we establish the consistency property for the proposed estimator.","abstract_has_math":false,"creators":["Mu, Yunming"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["He, Xuming"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T16:02:43Z","date_published":"2015-09-28T16:02:43Z","updated_at":"2026-07-22T22:26:30Z","subjects":["Statistics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3199092"],"render_values":[{"text":"(MiAaPQ)AAI3199092","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/87401","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["He, Xuming"]},{"key":"dc:creator","label":"Author","values":["Mu, Yunming"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T16:02:43Z","10000-01-01","2005"]},{"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"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/87401","(MiAaPQ)AAI3199092"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, we consider a family of parametric power transformations for the dependent variable such that a linear or partially linear quantile regression model holds after transformation. The two models being considered are the power-transformed linear quantile regression model and power-transformed partially linear quantile regression model, respectively. We use a cusum process of residuals to measure lack of fit for a given quantile function. A power transformation is chosen to minimize the lack of fit. For the power-transformed linear quantile regression model, we show that the proposed estimator is consistent and asymptotically normal under some mild conditions. We demonstrate that the proposed approach works better than competing methods in the presence of heteroscedasticity and heavy-tails. Inferences about the transformation parameter and about the covariate effects are considered mathematically as well as empirically. A test for the adequacy of the power-transformation models is also proposed. For the power-transformed partially linear quantile regression model, we establish the consistency property for the proposed estimator.","Made available in DSpace on 2015-09-28T16:02:43Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3199092.pdf: 2405111 bytes, checksum: 50b06ffc9d4fb6177c53046a9b98728b (MD5) Previous issue date: 2005","Embargo set by: Seth Robbins for item 88682 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","99 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2005."]},{"key":"dc:title","label":"Title","values":["Power Transformation Towards Linear or Partially Linear Quantile Regression Models"]}]}],"canonical_facts":{"dc:contributor":["He, Xuming"],"dc:creator":["Mu, Yunming"],"dc:date":["2015-09-28T16:02:43Z","10000-01-01","2005"],"dc:description":["In this thesis, we consider a family of parametric power transformations for the dependent variable such that a linear or partially linear quantile regression model holds after transformation. The two models being considered are the power-transformed linear quantile regression model and power-transformed partially linear quantile regression model, respectively. We use a cusum process of residuals to measure lack of fit for a given quantile function. A power transformation is chosen to minimize the lack of fit. For the power-transformed linear quantile regression model, we show that the proposed estimator is consistent and asymptotically normal under some mild conditions. We demonstrate that the proposed approach works better than competing methods in the presence of heteroscedasticity and heavy-tails. Inferences about the transformation parameter and about the covariate effects are considered mathematically as well as empirically. A test for the adequacy of the power-transformation models is also proposed. For the power-transformed partially linear quantile regression model, we establish the consistency property for the proposed estimator.","Made available in DSpace on 2015-09-28T16:02:43Z (GMT). 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