{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23507"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23507","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Inferences on high-dimensional data","abstract":"\"Dimension reduction techniques are important in the problem of regression and prediction when the nominal number of predicting variables is greater than the number of observations. Two methods, principal components analysis (PCA) and partial least squares (PLS), are used for regression and classification. We show that the null distribution of the PLS \"\"f-test\"\" statistic, which is obtained from one factor PLS regression, depends heavily on the design. A simulation method is suggested to compute the appropriate significant level of the \"\"f-test\"\". Some of the statistical properties of the composite dimensional reduction procedures are derived.\"","abstract_html":""Dimension reduction techniques are important in the problem of regression and prediction when the nominal number of predicting variables is greater than the number of observations. Two methods, principal components analysis (PCA) and partial least squares (PLS), are used for regression and classification. We show that the null distribution of the PLS ""f-test"" statistic, which is obtained from one factor PLS regression, depends heavily on the design. A simulation method is suggested to compute the appropriate significant level of the ""f-test"". Some of the statistical properties of the composite dimensional reduction procedures are derived."","abstract_has_math":false,"creators":["Guo, Sha-Lin"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["Simpson, Douglas G."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T14:16:46Z","date_published":"2011-05-07T14:16:46Z","updated_at":"2026-07-22T22:25:22Z","subjects":["Statistics"],"languages":["eng"],"rights":["Copyright 1990 Guo, Sha-Lin"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9114251","(UMI)AAI9114251"],"render_values":[{"text":"AAI9114251","href":null,"code":true},{"text":"(UMI)AAI9114251","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23507","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Simpson, Douglas G."]},{"key":"dc:creator","label":"Author","values":["Guo, Sha-Lin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:16:46Z","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 Guo, Sha-Lin"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9114251","(UMI)AAI9114251","http://hdl.handle.net/2142/23507"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"Dimension reduction techniques are important in the problem of regression and prediction when the nominal number of predicting variables is greater than the number of observations. 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The approach appears to be useful in determining which components are responsible for the classification.","Made available in DSpace on 2011-05-07T14:16:46Z (GMT). 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Two methods, principal components analysis (PCA) and partial least squares (PLS), are used for regression and classification. We show that the null distribution of the PLS \"\"f-test\"\" statistic, which is obtained from one factor PLS regression, depends heavily on the design. A simulation method is suggested to compute the appropriate significant level of the \"\"f-test\"\". Some of the statistical properties of the composite dimensional reduction procedures are derived.\"","In classification, it is shown that the linear discriminant rule based on PLS in the two groups case corresponds to assigning the covariance structure which is spherical. This suggests that some improvement might be possible by more flexible modelling of the covariance structure. We use a time series model for the covariance. This leads to a parametric quadratic classifier. 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