Optimization of ridge parameters in multivariate generalized ridge regression by plug-in methods
Generalized ridge (GR) regression for an univariate linear model was proposed simultaneously with ridge regression by Hoerl and Kennard (1970). In this paper, we deal with a GR regression for a multivariate linear model, referred to as a multivariate GR (MGR) regression. From the viewpoint of reduci...
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| Veröffentlicht in: | Hiroshima mathematical journal 2012-11, Vol.42 (3), p.301-324 |
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| container_title | Hiroshima mathematical journal |
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| creator | Nagai, Isamu Yanagihara, Hirokazu Satoh, Kenichi |
| description | Generalized ridge (GR) regression for an univariate linear model was
proposed simultaneously with ridge regression by Hoerl and Kennard (1970). In this
paper, we deal with a GR regression for a multivariate linear model, referred to as a
multivariate GR (MGR) regression. From the viewpoint of reducing the mean squared
error (MSE) of a predicted value, many authors have proposed several GR estimators
consisting of ridge parameters optimized by non-iterative methods. By expanding their
optimizations of ridge parameters to the multiple response case, we derive some MGR
estimators with ridge parameters optimized by the plug-in method. We analytically
compare obtained MGR estimators with existing MGR estimators, and numerical
studies are also given for an illustration. |
| doi_str_mv | 10.32917/hmj/1355238371 |
| format | Article |
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proposed simultaneously with ridge regression by Hoerl and Kennard (1970). In this
paper, we deal with a GR regression for a multivariate linear model, referred to as a
multivariate GR (MGR) regression. From the viewpoint of reducing the mean squared
error (MSE) of a predicted value, many authors have proposed several GR estimators
consisting of ridge parameters optimized by non-iterative methods. By expanding their
optimizations of ridge parameters to the multiple response case, we derive some MGR
estimators with ridge parameters optimized by the plug-in method. We analytically
compare obtained MGR estimators with existing MGR estimators, and numerical
studies are also given for an illustration.</description><identifier>ISSN: 0018-2079</identifier><identifier>DOI: 10.32917/hmj/1355238371</identifier><language>eng</language><publisher>Hiroshima University, Department of Mathematics</publisher><subject>62H12 ; 62J07 ; Generalized ridge regression ; Mallows’ C_p statistic ; model selection ; multivariate linear regression model ; non-iterative estimation ; plug-in method</subject><ispartof>Hiroshima mathematical journal, 2012-11, Vol.42 (3), p.301-324</ispartof><rights>Copyright 2012 Hiroshima University, Department of Mathematics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c405t-6100b2160485a2498db74582033da9deab0fa09162eeb11ec03ab929c8ff982b3</citedby><cites>FETCH-LOGICAL-c405t-6100b2160485a2498db74582033da9deab0fa09162eeb11ec03ab929c8ff982b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,778,782,880,883,924,27907,27908</link.rule.ids></links><search><creatorcontrib>Nagai, Isamu</creatorcontrib><creatorcontrib>Yanagihara, Hirokazu</creatorcontrib><creatorcontrib>Satoh, Kenichi</creatorcontrib><title>Optimization of ridge parameters in multivariate generalized ridge regression by plug-in methods</title><title>Hiroshima mathematical journal</title><description>Generalized ridge (GR) regression for an univariate linear model was
proposed simultaneously with ridge regression by Hoerl and Kennard (1970). In this
paper, we deal with a GR regression for a multivariate linear model, referred to as a
multivariate GR (MGR) regression. From the viewpoint of reducing the mean squared
error (MSE) of a predicted value, many authors have proposed several GR estimators
consisting of ridge parameters optimized by non-iterative methods. By expanding their
optimizations of ridge parameters to the multiple response case, we derive some MGR
estimators with ridge parameters optimized by the plug-in method. We analytically
compare obtained MGR estimators with existing MGR estimators, and numerical
studies are also given for an illustration.</description><subject>62H12</subject><subject>62J07</subject><subject>Generalized ridge regression</subject><subject>Mallows’ C_p statistic</subject><subject>model selection</subject><subject>multivariate linear regression model</subject><subject>non-iterative estimation</subject><subject>plug-in method</subject><issn>0018-2079</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNpdkDtPwzAURj2ARCnMrP4Dodd2HvYGqnhUqtSFzsGOb1JXSRPZLlL762lpBBLTJ13dc4ZDyAODR8EVK2abbjtjIsu4kKJgV2QCwGTCoVA35DaELYAocplNyOdqiK5zRx1dv6N9Tb2zDdJBe91hRB-o29Fu30b3pb3TEWmDO_S6dUe047PHxmMIZ4E50KHdN8kZwrjpbbgj17VuA96POyXr15eP-XuyXL0t5s_LpEohi0nOAAxnOaQy0zxV0poizSQHIaxWFrWBWoNiOUc0jGEFQhvFVSXrWkluxJQ8XbyD77dYRdxXrbPl4F2n_aHstSvn6-V4HedUqfyrdFLMLorK9yF4rH9pBuVP1__EN9M4cJM</recordid><startdate>20121101</startdate><enddate>20121101</enddate><creator>Nagai, Isamu</creator><creator>Yanagihara, Hirokazu</creator><creator>Satoh, Kenichi</creator><general>Hiroshima University, Department of Mathematics</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20121101</creationdate><title>Optimization of ridge parameters in multivariate generalized ridge regression by plug-in methods</title><author>Nagai, Isamu ; Yanagihara, Hirokazu ; Satoh, Kenichi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c405t-6100b2160485a2498db74582033da9deab0fa09162eeb11ec03ab929c8ff982b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>62H12</topic><topic>62J07</topic><topic>Generalized ridge regression</topic><topic>Mallows’ C_p statistic</topic><topic>model selection</topic><topic>multivariate linear regression model</topic><topic>non-iterative estimation</topic><topic>plug-in method</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nagai, Isamu</creatorcontrib><creatorcontrib>Yanagihara, Hirokazu</creatorcontrib><creatorcontrib>Satoh, Kenichi</creatorcontrib><collection>CrossRef</collection><jtitle>Hiroshima mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nagai, Isamu</au><au>Yanagihara, Hirokazu</au><au>Satoh, Kenichi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimization of ridge parameters in multivariate generalized ridge regression by plug-in methods</atitle><jtitle>Hiroshima mathematical journal</jtitle><date>2012-11-01</date><risdate>2012</risdate><volume>42</volume><issue>3</issue><spage>301</spage><epage>324</epage><pages>301-324</pages><issn>0018-2079</issn><abstract>Generalized ridge (GR) regression for an univariate linear model was
proposed simultaneously with ridge regression by Hoerl and Kennard (1970). In this
paper, we deal with a GR regression for a multivariate linear model, referred to as a
multivariate GR (MGR) regression. From the viewpoint of reducing the mean squared
error (MSE) of a predicted value, many authors have proposed several GR estimators
consisting of ridge parameters optimized by non-iterative methods. By expanding their
optimizations of ridge parameters to the multiple response case, we derive some MGR
estimators with ridge parameters optimized by the plug-in method. We analytically
compare obtained MGR estimators with existing MGR estimators, and numerical
studies are also given for an illustration.</abstract><pub>Hiroshima University, Department of Mathematics</pub><doi>10.32917/hmj/1355238371</doi><tpages>24</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Hiroshima mathematical journal, 2012-11, Vol.42 (3), p.301-324 |
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| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_hmj_1355238371 |
| source | Project Euclid Open Access; Open Access Titles of Japan; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | 62H12 62J07 Generalized ridge regression Mallows’ C_p statistic model selection multivariate linear regression model non-iterative estimation plug-in method |
| title | Optimization of ridge parameters in multivariate generalized ridge regression by plug-in methods |
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