Covariate Information Matrix for Sufficient Dimension Reduction
Building upon recent research on the applications of the density information matrix, we develop a tool for sufficient dimension reduction (SDR) in regression problems called covariate information matrix (CIM). CIM exhaustively identifies the central subspace (CS) and provides a rank ordering of the...
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| Veröffentlicht in: | Journal of the American Statistical Association 2019-10, Vol.114 (528), p.1752-1764 |
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| creator | Yao, Weixin Nandy, Debmalya Lindsay, Bruce G. Chiaromonte, Francesca |
| description | Building upon recent research on the applications of the density information matrix, we develop a tool for sufficient dimension reduction (SDR) in regression problems called covariate information matrix (CIM). CIM exhaustively identifies the central subspace (CS) and provides a rank ordering of the reduced covariates in terms of their regression information. Compared to other popular SDR methods, CIM does not require distributional assumptions on the covariates, or estimation of the mean regression function. CIM is implemented via eigen-decomposition of a matrix estimated with a previously developed efficient nonparametric density estimation technique. We also propose a bootstrap-based diagnostic plot for estimating the dimension of the CS. Results of simulations and real data applications demonstrate superior or competitive performance of CIM compared to that of some other SDR methods.
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| doi_str_mv | 10.1080/01621459.2018.1515080 |
| format | Article |
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Supplementary materials
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Supplementary materials
for this article are available online.</description><subject>Bootstrap</subject><subject>Central subspace</subject><subject>Density</subject><subject>Density information matrix</subject><subject>Diagnostic systems</subject><subject>Estimating techniques</subject><subject>Fisher information matrix</subject><subject>Nonparametric density estimation</subject><subject>Nonparametric statistics</subject><subject>Reduction</subject><subject>Regression</subject><subject>Regression analysis</subject><subject>Statistical methods</subject><subject>Statistics</subject><subject>Sufficient dimension reduction</subject><issn>0162-1459</issn><issn>1537-274X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEQgIMoWKs_QVjwvDWTbDbpSaW-ChXBB3gL2TSBlHZTk6zaf2-WrVfnMjDzzQzzIXQOeAJY4EsMNYGKTScEg5gAA5arB2gEjPKS8OrjEI16puyhY3QS4wrn4EKM0NXMf6ngVDLFvLU-bFRyvi2eVArup8iF4rWz1mln2lTcuo1pY99_MctO9-QpOrJqHc3ZPo_R-_3d2-yxXDw_zGc3i1JTDqnUuKkbBiAYV0bQimJjsLC1UZxOoQJCKoN1w4lS-RUCmmJNGwu1oFbwKaNjdDHs3Qb_2ZmY5Mp3oc0nJaGUUMYEIZliA6WDjzEYK7fBbVTYScCydyX_XMneldy7ynPXw5wbHHz7sF7KpHZrH2xQrXZR0v9X_AKXN27k</recordid><startdate>20191002</startdate><enddate>20191002</enddate><creator>Yao, Weixin</creator><creator>Nandy, Debmalya</creator><creator>Lindsay, Bruce G.</creator><creator>Chiaromonte, Francesca</creator><general>Taylor & Francis</general><general>Taylor & Francis Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8BJ</scope><scope>FQK</scope><scope>JBE</scope><scope>K9.</scope></search><sort><creationdate>20191002</creationdate><title>Covariate Information Matrix for Sufficient Dimension Reduction</title><author>Yao, Weixin ; Nandy, Debmalya ; Lindsay, Bruce G. ; Chiaromonte, Francesca</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c371t-c0b6b511857ae83430ee08f6ea739141224e0cb72aa21421c30c3bf1683f87953</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Bootstrap</topic><topic>Central subspace</topic><topic>Density</topic><topic>Density information matrix</topic><topic>Diagnostic systems</topic><topic>Estimating techniques</topic><topic>Fisher information matrix</topic><topic>Nonparametric density estimation</topic><topic>Nonparametric statistics</topic><topic>Reduction</topic><topic>Regression</topic><topic>Regression analysis</topic><topic>Statistical methods</topic><topic>Statistics</topic><topic>Sufficient dimension reduction</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yao, Weixin</creatorcontrib><creatorcontrib>Nandy, Debmalya</creatorcontrib><creatorcontrib>Lindsay, Bruce G.</creatorcontrib><creatorcontrib>Chiaromonte, Francesca</creatorcontrib><collection>CrossRef</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>International Bibliography of the Social Sciences</collection><collection>International Bibliography of the Social Sciences</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><jtitle>Journal of the American Statistical Association</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yao, Weixin</au><au>Nandy, Debmalya</au><au>Lindsay, Bruce G.</au><au>Chiaromonte, Francesca</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Covariate Information Matrix for Sufficient Dimension Reduction</atitle><jtitle>Journal of the American Statistical Association</jtitle><date>2019-10-02</date><risdate>2019</risdate><volume>114</volume><issue>528</issue><spage>1752</spage><epage>1764</epage><pages>1752-1764</pages><issn>0162-1459</issn><eissn>1537-274X</eissn><abstract>Building upon recent research on the applications of the density information matrix, we develop a tool for sufficient dimension reduction (SDR) in regression problems called covariate information matrix (CIM). CIM exhaustively identifies the central subspace (CS) and provides a rank ordering of the reduced covariates in terms of their regression information. Compared to other popular SDR methods, CIM does not require distributional assumptions on the covariates, or estimation of the mean regression function. CIM is implemented via eigen-decomposition of a matrix estimated with a previously developed efficient nonparametric density estimation technique. We also propose a bootstrap-based diagnostic plot for estimating the dimension of the CS. Results of simulations and real data applications demonstrate superior or competitive performance of CIM compared to that of some other SDR methods.
Supplementary materials
for this article are available online.</abstract><cop>Alexandria</cop><pub>Taylor & Francis</pub><doi>10.1080/01621459.2018.1515080</doi><tpages>13</tpages></addata></record> |
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| subjects | Bootstrap Central subspace Density Density information matrix Diagnostic systems Estimating techniques Fisher information matrix Nonparametric density estimation Nonparametric statistics Reduction Regression Regression analysis Statistical methods Statistics Sufficient dimension reduction |
| title | Covariate Information Matrix for Sufficient Dimension Reduction |
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