{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23742"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23742","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Recursive methods for statistical prediction with applications","abstract":"Recursive methods for solving the nonparametric regression problem in the GLIMs and computing the Best Linear Unbiased Predictors are discussed here. An iterated state space algorithm is introduced to compute the generalized smoothing spline estimate, and it is especially useful in calculating the leave-one-out estimates. Two cross validation functions (Kullback-Leibler and least squares cross validation) for estimating the smoothing parameter in the generalized smoothing splines are discussed. The simulation results showed that these two cross validation functions performed quite well.","abstract_html":"Recursive methods for solving the nonparametric regression problem in the GLIMs and computing the Best Linear Unbiased Predictors are discussed here. An iterated state space algorithm is introduced to compute the generalized smoothing spline estimate, and it is especially useful in calculating the leave-one-out estimates. Two cross validation functions (Kullback-Leibler and least squares cross validation) for estimating the smoothing parameter in the generalized smoothing splines are discussed. The simulation results showed that these two cross validation functions performed quite well.","abstract_has_math":false,"creators":["Chang, Yue-Fang"],"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":"2011-05-07T14:25:23Z","date_published":"2011-05-07T14:25:23Z","updated_at":"2026-07-22T22:25:22Z","subjects":["Statistics"],"languages":["eng"],"rights":["Copyright 1991 Chang, Yue-Fang"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9124392","(UMI)AAI9124392"],"render_values":[{"text":"AAI9124392","href":null,"code":true},{"text":"(UMI)AAI9124392","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23742","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":["Chang, Yue-Fang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:25:23Z","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 Chang, Yue-Fang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9124392","(UMI)AAI9124392","http://hdl.handle.net/2142/23742"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Recursive methods for solving the nonparametric regression problem in the GLIMs and computing the Best Linear Unbiased Predictors are discussed here. An iterated state space algorithm is introduced to compute the generalized smoothing spline estimate, and it is especially useful in calculating the leave-one-out estimates. Two cross validation functions (Kullback-Leibler and least squares cross validation) for estimating the smoothing parameter in the generalized smoothing splines are discussed. The simulation results showed that these two cross validation functions performed quite well.","Best Linear Unbiased Predictors can be used to predict the values of a random function from the observed values. It is of interest to have an efficient algorithm to compute the predictions when observations are taken sequentially, rather than performing the linear algebra from the beginning. An updatable algorithm, which is based on combining the updating procedures of Cholesky and Q-R decomposition, is introduced to compute the predictions and mean squared error of the predictions when more observations are taken.","Made available in DSpace on 2011-05-07T14:25:23Z (GMT). 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An iterated state space algorithm is introduced to compute the generalized smoothing spline estimate, and it is especially useful in calculating the leave-one-out estimates. Two cross validation functions (Kullback-Leibler and least squares cross validation) for estimating the smoothing parameter in the generalized smoothing splines are discussed. The simulation results showed that these two cross validation functions performed quite well.","Best Linear Unbiased Predictors can be used to predict the values of a random function from the observed values. It is of interest to have an efficient algorithm to compute the predictions when observations are taken sequentially, rather than performing the linear algebra from the beginning. An updatable algorithm, which is based on combining the updating procedures of Cholesky and Q-R decomposition, is introduced to compute the predictions and mean squared error of the predictions when more observations are taken.","Made available in DSpace on 2011-05-07T14:25:23Z (GMT). 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