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INVERSE REGRESSION FOR LONGITUDINAL DATA
Sliced inverse regression (Duan and Li [Ann. Statist. 19 (1991) 505-530], Li [J. Amer. Statist. Assoc. 86 (1991) 316-342]) is an appealing dimension reduction method for regression models with multivariate covariates. It has been extended by Ferré and Yao [Statistics 37 (2003) 475-488, Statist. Sini...
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| Published in: | The Annals of statistics 2014-04, Vol.42 (2), p.563-591 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c374t-c8b44ec242f427295d168eeb7f4e95b22bf1a0be3243ee7dccb9f469ebc8ff2d3 |
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| cites | cdi_FETCH-LOGICAL-c374t-c8b44ec242f427295d168eeb7f4e95b22bf1a0be3243ee7dccb9f469ebc8ff2d3 |
| container_end_page | 591 |
| container_issue | 2 |
| container_start_page | 563 |
| container_title | The Annals of statistics |
| container_volume | 42 |
| creator | Jiang, Ci-Ren Yu, Wei Wang, Jane-Ling |
| description | Sliced inverse regression (Duan and Li [Ann. Statist. 19 (1991) 505-530], Li [J. Amer. Statist. Assoc. 86 (1991) 316-342]) is an appealing dimension reduction method for regression models with multivariate covariates. It has been extended by Ferré and Yao [Statistics 37 (2003) 475-488, Statist. Sinica 15 (2005) 665-683] and Hsing and Ren [Ann. Statist. 37 (2009) 726-755] to functional covariates where the whole trajectories of random functional covariates are completely observed. The focus of this paper is to develop sliced inverse regression for intermittently and sparsely measured longitudinal covariates. We develop asymptotic theory for the new procedure and show, under some regularity conditions, that the estimated directions attain the optimal rate of convergence. Simulation studies and data analysis are also provided to demonstrate the performance of our method. |
| doi_str_mv | 10.1214/13-AOS1193 |
| format | article |
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Statist. 19 (1991) 505-530], Li [J. Amer. Statist. Assoc. 86 (1991) 316-342]) is an appealing dimension reduction method for regression models with multivariate covariates. It has been extended by Ferré and Yao [Statistics 37 (2003) 475-488, Statist. Sinica 15 (2005) 665-683] and Hsing and Ren [Ann. Statist. 37 (2009) 726-755] to functional covariates where the whole trajectories of random functional covariates are completely observed. The focus of this paper is to develop sliced inverse regression for intermittently and sparsely measured longitudinal covariates. We develop asymptotic theory for the new procedure and show, under some regularity conditions, that the estimated directions attain the optimal rate of convergence. Simulation studies and data analysis are also provided to demonstrate the performance of our method.</description><identifier>ISSN: 0090-5364</identifier><identifier>EISSN: 2168-8966</identifier><identifier>DOI: 10.1214/13-AOS1193</identifier><language>eng</language><publisher>Hayward: Institute of Mathematical Statistics</publisher><subject>62G05 ; 62G08 ; 62G20 ; Asymptotic methods ; Covariance ; Covariance operator ; Data analysis ; Data smoothing ; dimension reduction ; Dimensionality reduction ; Eigenfunctions ; Eigenvalues ; Estimating techniques ; Estimation methods ; Fecundity ; functional data analysis ; Inverse problems ; Linear regression ; local polynomial smoothing ; Longitudinal data ; Mathematical models ; Multivariate analysis ; Regression analysis ; regularization ; sparse data ; Studies</subject><ispartof>The Annals of statistics, 2014-04, Vol.42 (2), p.563-591</ispartof><rights>Copyright © 2014 Institute of Mathematical Statistics</rights><rights>Copyright Institute of Mathematical Statistics Apr 2014</rights><rights>Copyright 2014 Institute of Mathematical Statistics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c374t-c8b44ec242f427295d168eeb7f4e95b22bf1a0be3243ee7dccb9f469ebc8ff2d3</citedby><cites>FETCH-LOGICAL-c374t-c8b44ec242f427295d168eeb7f4e95b22bf1a0be3243ee7dccb9f469ebc8ff2d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/43556296$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/43556296$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,777,781,882,922,27905,27906,58219,58452</link.rule.ids></links><search><creatorcontrib>Jiang, Ci-Ren</creatorcontrib><creatorcontrib>Yu, Wei</creatorcontrib><creatorcontrib>Wang, Jane-Ling</creatorcontrib><title>INVERSE REGRESSION FOR LONGITUDINAL DATA</title><title>The Annals of statistics</title><description>Sliced inverse regression (Duan and Li [Ann. 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Simulation studies and data analysis are also provided to demonstrate the performance of our method.</description><subject>62G05</subject><subject>62G08</subject><subject>62G20</subject><subject>Asymptotic methods</subject><subject>Covariance</subject><subject>Covariance operator</subject><subject>Data analysis</subject><subject>Data smoothing</subject><subject>dimension reduction</subject><subject>Dimensionality reduction</subject><subject>Eigenfunctions</subject><subject>Eigenvalues</subject><subject>Estimating techniques</subject><subject>Estimation methods</subject><subject>Fecundity</subject><subject>functional data analysis</subject><subject>Inverse problems</subject><subject>Linear regression</subject><subject>local polynomial smoothing</subject><subject>Longitudinal data</subject><subject>Mathematical models</subject><subject>Multivariate analysis</subject><subject>Regression analysis</subject><subject>regularization</subject><subject>sparse data</subject><subject>Studies</subject><issn>0090-5364</issn><issn>2168-8966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNo9kM9LwzAcxYMoOKcX70LBiwjV_GrS3CxbNwulhXbzGpo0gZVpZ9Id_O_tWNnpwZcP773vA-ARwTeEEX1HJEzKGiFBrsAMIxaHsWDsGswgFDCMCKO34M77DkIYCUpm4CUrvtKqToMqXVdpXWdlEazKKsjLYp1ttsusSPJgmWySe3Bjm703D5POwXaVbhafYV6us0WSh5pwOoQ6VpQajSm2FHMsonYsYYzilhoRKYyVRQ1UhmBKjOGt1kpYyoRROrYWt2QOPs6-B9d3Rg_mqPe7Vh7c7rtxf7JvdnKxzafrJE3vJaKnlzDicLR4vlj8Ho0fZNcf3c_YWiIejwCjhI_U65nSrvfeGXvJQFCexpSIyGnMEX46w50fenchKYkihgUj_6sjbGM</recordid><startdate>20140401</startdate><enddate>20140401</enddate><creator>Jiang, Ci-Ren</creator><creator>Yu, Wei</creator><creator>Wang, Jane-Ling</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20140401</creationdate><title>INVERSE REGRESSION FOR LONGITUDINAL DATA</title><author>Jiang, Ci-Ren ; Yu, Wei ; Wang, Jane-Ling</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c374t-c8b44ec242f427295d168eeb7f4e95b22bf1a0be3243ee7dccb9f469ebc8ff2d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>62G05</topic><topic>62G08</topic><topic>62G20</topic><topic>Asymptotic methods</topic><topic>Covariance</topic><topic>Covariance operator</topic><topic>Data analysis</topic><topic>Data smoothing</topic><topic>dimension reduction</topic><topic>Dimensionality reduction</topic><topic>Eigenfunctions</topic><topic>Eigenvalues</topic><topic>Estimating techniques</topic><topic>Estimation methods</topic><topic>Fecundity</topic><topic>functional data analysis</topic><topic>Inverse problems</topic><topic>Linear regression</topic><topic>local polynomial smoothing</topic><topic>Longitudinal data</topic><topic>Mathematical models</topic><topic>Multivariate analysis</topic><topic>Regression analysis</topic><topic>regularization</topic><topic>sparse data</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jiang, Ci-Ren</creatorcontrib><creatorcontrib>Yu, Wei</creatorcontrib><creatorcontrib>Wang, Jane-Ling</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>The Annals of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jiang, Ci-Ren</au><au>Yu, Wei</au><au>Wang, Jane-Ling</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>INVERSE REGRESSION FOR LONGITUDINAL DATA</atitle><jtitle>The Annals of statistics</jtitle><date>2014-04-01</date><risdate>2014</risdate><volume>42</volume><issue>2</issue><spage>563</spage><epage>591</epage><pages>563-591</pages><issn>0090-5364</issn><eissn>2168-8966</eissn><abstract>Sliced inverse regression (Duan and Li [Ann. 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| identifier | ISSN: 0090-5364 |
| ispartof | The Annals of statistics, 2014-04, Vol.42 (2), p.563-591 |
| issn | 0090-5364 2168-8966 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_aos_1400592170 |
| source | JSTOR-E-Journals; Project Euclid |
| subjects | 62G05 62G08 62G20 Asymptotic methods Covariance Covariance operator Data analysis Data smoothing dimension reduction Dimensionality reduction Eigenfunctions Eigenvalues Estimating techniques Estimation methods Fecundity functional data analysis Inverse problems Linear regression local polynomial smoothing Longitudinal data Mathematical models Multivariate analysis Regression analysis regularization sparse data Studies |
| title | INVERSE REGRESSION FOR LONGITUDINAL DATA |
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