{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T17:10:44Z","timestamp":1777137044975,"version":"3.51.4"},"reference-count":29,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2023,3,11]],"date-time":"2023-03-11T00:00:00Z","timestamp":1678492800000},"content-version":"vor","delay-in-days":3412,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1000354"],"award-info":[{"award-number":["DMS-1000354"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1206693"],"award-info":[{"award-number":["DMS-1206693"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000065","name":"National Institute of Neurological Disorders and Stroke","doi-asserted-by":"publisher","award":["R01-NS073671"],"award-info":[{"award-number":["R01-NS073671"]}],"id":[{"id":"10.13039\/100000065","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Laboratory of Mathematical Economics, Ministry of Education"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11071077"],"award-info":[{"award-number":["11071077"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11371236"],"award-info":[{"award-number":["11371236"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003395","name":"Shanghai Municipal Education Commission","doi-asserted-by":"publisher","award":["13ZZ055"],"award-info":[{"award-number":["13ZZ055"]}],"id":[{"id":"10.13039\/501100003395","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003399","name":"Science and Technology Commission of Shanghai Municipality","doi-asserted-by":"publisher","award":["12PJ1403200"],"award-info":[{"award-number":["12PJ1403200"]}],"id":[{"id":"10.13039\/501100003399","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002338","name":"Ministry of Education of China","doi-asserted-by":"publisher","award":["NCET-12-0901"],"award-info":[{"award-number":["NCET-12-0901"]}],"id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,11,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We investigate the estimation efficiency of the central mean subspace in the framework of sufficient dimension reduction. We derive the semiparametric efficient score and study its practical applicability. Despite the difficulty caused by the potential high dimension issue in the variance component, we show that locally efficient estimators can be constructed in practice. We conduct simulation studies and a real data analysis to demonstrate the finite sample performance and gain in efficiency of the proposed estimators in comparison with several existing methods.<\/jats:p>","DOI":"10.1111\/rssb.12044","type":"journal-article","created":{"date-parts":[[2013,11,7]],"date-time":"2013-11-07T04:56:40Z","timestamp":1383800200000},"page":"885-901","source":"Crossref","is-referenced-by-count":38,"title":["On Estimation Efficiency of the Central Mean Subspace"],"prefix":"10.1093","volume":"76","author":[{"given":"Yanyuan","family":"Ma","sequence":"first","affiliation":[{"name":"Texas A&M University , College Station , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liping","family":"Zhu","sequence":"additional","affiliation":[{"name":"Shanghai University of Finance and Economics People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2013,11,6]]},"reference":[{"key":"2023031201061528900_","volume-title":"Data Analysis and Decision Making with Microsoft Excel","author":"Albright","year":"1999"},{"key":"2023031201061528900_","volume-title":"Efficient and Adaptive Estimation for Semiparametric Models","author":"Bickel","year":"1993"},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1214\/aos\/1021379861","article-title":"Dimension reduction for conditional mean in regression","volume":"30","author":"Cook","year":"2002","journal-title":"Ann. Statist."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"2501","DOI":"10.1214\/009053604000000661","article-title":"Determining the dimension of iterative Hessian transformation","volume":"32","author":"Cook","year":"2004","journal-title":"Ann. Statist."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1198\/016214504000001501","article-title":"Sufficient dimension reduction via inverse regression: a minimum discrepancy approach","volume":"100","author":"Cook","year":"2005","journal-title":"J. Am. Statist. Ass."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1093\/biomet\/93.1.65","article-title":"Using intraslice covariances for improved estimation of the central subspace in regression","volume":"93","author":"Cook","year":"2006","journal-title":"Biometrika"},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/S0047-259X(02)00046-5","article-title":"Efficient estimation in conditional single-index regression","volume":"86","author":"Delecroix","year":"2003","journal-title":"J. Multiv. Anal."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1093\/biomet\/asq016","article-title":"Dimension reduction for non-elliptically distributed predictors: second-order moments","volume":"97","author":"Dong","year":"2010","journal-title":"Biometrika"},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1214\/aos\/996986505","article-title":"Generalized likelihood ratio statistics and Wilks phenomenon","volume":"29","author":"Fan","year":"2001","journal-title":"Ann. Statist."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1214\/aos\/1176349020","article-title":"Optimal smoothing in single index-models","volume":"21","author":"H\u00e4rdle","year":"1993","journal-title":"Ann. Statist."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"1632","DOI":"10.1080\/01621459.1996.10476732","article-title":"Direct semiparametric estimation of single-index models with discrete covariates","volume":"91","author":"Horowitz","year":"1996","journal-title":"J. Am. Statist. Ass."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1080\/01621459.1991.10475035","article-title":"Sliced inverse regression for dimension reduction (with discussion)","volume":"86","author":"Li","year":"1991","journal-title":"J. Am. Statist. Ass."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1080\/01621459.1992.10476258","article-title":"On principal Hessian directions for data visualization and dimension reduction: another application of Stein's lemma","volume":"87","author":"Li","year":"1992","journal-title":"J. Am. Statist. Ass."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"1636","DOI":"10.1214\/aos\/1065705121","article-title":"Dimension reduction for conditional mean in regression with categorical predictors","volume":"31","author":"Li","year":"2003","journal-title":"Ann. Statist."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1214\/08-AOS598","article-title":"Dimension reduction for non-elliptically distributed predictors","volume":"37","author":"Li","year":"2009","journal-title":"Ann. Statist."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1214\/aos\/1176347254","article-title":"Regression analysis under link violation","volume":"17","author":"Li","year":"1989","journal-title":"Ann. Statist."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"1188","DOI":"10.1198\/jasa.2010.tm09643","article-title":"Groupwise dimension reduction","volume":"105","author":"Li","year":"2010","journal-title":"J. Am. Statist. Ass."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1093\/biomet\/93.1.75","article-title":"Efficient semiparametric estimator for heteroscedastic partially-linear models","volume":"93","author":"Ma","year":"2006","journal-title":"Biometrika"},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1080\/01621459.2011.646925","article-title":"A semiparametric approach to dimension reduction","volume":"107","author":"Ma","year":"2012","journal-title":"J. Am. Statist. Ass."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1093\/biomet\/ass075","article-title":"Efficiency loss caused by linearity condition in dimension reduction","volume":"100","author":"Ma","year":"2013","journal-title":"Biometrika"},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1198\/016214506000001103","article-title":"Efficient estimation of population-level summaries in general semiparametric regression models","volume":"102","author":"Maity","year":"2007","journal-title":"J. Am. Statist. Ass."},{"key":"2023031201061528900_","volume-title":"Semiparametric Theory and Missing Data","author":"Tsiatis","year":"2006"},{"key":"2023031201061528900_","first-page":"797","article-title":"Backfitting versus profiling in general criterion functions","volume":"17","author":"Van Keilegom","year":"2007","journal-title":"Statist. Sin."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"2654","DOI":"10.1214\/009053607000000352","article-title":"A constructive approach to the estimation of dimension reduction directions","volume":"35","author":"Xia","year":"2007","journal-title":"Ann. Statist."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"1631","DOI":"10.1198\/016214508000000805","article-title":"A multiple-index model and dimension reduction","volume":"103","author":"Xia","year":"2008","journal-title":"J. Am. Statist. Ass."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1111\/1467-9868.03411","article-title":"An adaptive estimation of dimension reduction space (with discussion)","volume":"64","author":"Xia","year":"2002","journal-title":"J. R. Statist. Soc. B"},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1198\/016214503000000927","article-title":"Using the bootstrap to select one of a new class of dimension reduction methods","volume":"98","author":"Ye","year":"2003","journal-title":"J. Am. Statist. Ass."},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1093\/biomet\/asm003","article-title":"Optimal sufficient dimension reduction for the conditional mean in multivariate regressions","volume":"94","author":"Yoo","year":"2007","journal-title":"Biometrika"},{"key":"2023031201061528900_","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1198\/016214505000001285","article-title":"On sliced inverse regression with large dimensional covariates","volume":"101","author":"Zhu","year":"2006","journal-title":"J. Am. Statist. Ass."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Frssb.12044","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/76\/5\/885\/49506895\/jrsssb_76_5_885.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/76\/5\/885\/49506895\/jrsssb_76_5_885.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,6]],"date-time":"2023-07-06T07:24:57Z","timestamp":1688628297000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/76\/5\/885\/7075925"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,6]]},"references-count":29,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2013,11,6]]},"published-print":{"date-parts":[[2014,11,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12044","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2014,11]]},"published":{"date-parts":[[2013,11,6]]}}}