{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T10:51:48Z","timestamp":1774263108831,"version":"3.50.1"},"reference-count":44,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2019,12,1]],"date-time":"2019-12-01T00:00:00Z","timestamp":1575158400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2019,12,1]],"date-time":"2019-12-01T00:00:00Z","timestamp":1575158400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computational Statistics & Data Analysis"],"published-print":{"date-parts":[[2019,12]]},"DOI":"10.1016\/j.csda.2019.06.004","type":"journal-article","created":{"date-parts":[[2019,6,27]],"date-time":"2019-06-27T12:11:55Z","timestamp":1561637515000},"page":"144-154","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":17,"special_numbering":"C","title":["Robust sufficient dimension reduction via ball covariance"],"prefix":"10.1016","volume":"140","author":[{"given":"Jia","family":"Zhang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7444-6529","authenticated-orcid":false,"given":"Xin","family":"Chen","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"455","key":"10.1016\/j.csda.2019.06.004_b1","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1198\/016214501753208979","article-title":"Extending sliced inverse regression: The weighted chi-squared test","volume":"96","author":"Bura","year":"2001","journal-title":"J. Amer. Statist. Assoc."},{"issue":"515","key":"10.1016\/j.csda.2019.06.004_b2","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.1080\/01621459.2015.1093944","article-title":"Sufficient reductions in regressions with exponential family inverse predictors","volume":"111","author":"Bura","year":"2016","journal-title":"J. Amer. Statist. Assoc."},{"issue":"509","key":"10.1016\/j.csda.2019.06.004_b3","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1080\/01621459.2014.914440","article-title":"Sufficient reductions in regressions with elliptically contoured inverse predictors","volume":"110","author":"Bura","year":"2015","journal-title":"J. Amer. Statist. Assoc."},{"issue":"3","key":"10.1016\/j.csda.2019.06.004_b4","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1093\/biomet\/asv016","article-title":"Diagnostic studies in sufficient dimension reduction","volume":"102","author":"Chen","year":"2015","journal-title":"Biometrika"},{"issue":"2","key":"10.1016\/j.csda.2019.06.004_b5","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1080\/00401706.2017.1321583","article-title":"Efficient sparse estimate of sufficient dimension reduction in high dimension","volume":"60","author":"Chen","year":"2018","journal-title":"Technometrics"},{"issue":"425","key":"10.1016\/j.csda.2019.06.004_b6","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1080\/01621459.1994.10476459","article-title":"On the interpretation of regression plots","volume":"89","author":"Cook","year":"1994","journal-title":"J. Amer. Statist. Assoc."},{"issue":"435","key":"10.1016\/j.csda.2019.06.004_b7","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1080\/01621459.1996.10476968","article-title":"Graphics for regressions with a binary response","volume":"91","author":"Cook","year":"1996","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/j.csda.2019.06.004_b8","series-title":"Regression Graphics: Ideas for Studying Regressions Through Graphics","author":"Cook","year":"1998"},{"issue":"4","key":"10.1016\/j.csda.2019.06.004_b9","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1214\/08-STS275","article-title":"Principal fitted components for dimension reduction in regression","volume":"23","author":"Cook","year":"2008","journal-title":"Statist. Sci."},{"issue":"485","key":"10.1016\/j.csda.2019.06.004_b10","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1198\/jasa.2009.0106","article-title":"Likelihood-based sufficient dimension reduction","volume":"104","author":"Cook","year":"2009","journal-title":"J. Amer. Statist. Assoc."},{"issue":"3","key":"10.1016\/j.csda.2019.06.004_b11","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1198\/jcgs.2009.08005","article-title":"Dimension reduction in regressions with exponential family predictors","volume":"18","author":"Cook","year":"2009","journal-title":"J. Comput. Graph. Statist."},{"issue":"470","key":"10.1016\/j.csda.2019.06.004_b12","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. Amer. Statist. Assoc."},{"issue":"414","key":"10.1016\/j.csda.2019.06.004_b13","first-page":"328","article-title":"Sliced inverse regression for dimension reduction: Comment","volume":"86","author":"Cook","year":"1991","journal-title":"J. Amer. Statist. Assoc."},{"issue":"2","key":"10.1016\/j.csda.2019.06.004_b14","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1111\/1467-842X.00164","article-title":"Theory & methods: Special invited paper: Dimension reduction and visualization in discriminant analysis (with discussion)","volume":"43","author":"Cook","year":"2001","journal-title":"Aust. N. Z. J. Stat."},{"issue":"2","key":"10.1016\/j.csda.2019.06.004_b15","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1080\/00401706.2012.727746","article-title":"Robust sparse principal component analysis","volume":"55","author":"Croux","year":"2013","journal-title":"Technometrics"},{"key":"10.1016\/j.csda.2019.06.004_b16","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.jmva.2014.10.005","article-title":"Robust inverse regression for dimension reduction","volume":"134","author":"Dong","year":"2015","journal-title":"J. Multivariate Anal."},{"issue":"5","key":"10.1016\/j.csda.2019.06.004_b17","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1111\/j.1467-9868.2008.00674.x","article-title":"Sure independence screening for ultrahigh dimensional feature space","volume":"70","author":"Fan","year":"2008","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"10.1016\/j.csda.2019.06.004_b18","series-title":"Sure Independence Screening","author":"Fan","year":"2017"},{"key":"10.1016\/j.csda.2019.06.004_b19","series-title":"Advances in Neural Information Processing Systems","first-page":"585","article-title":"A kernel statistical test of independence","author":"Gretton","year":"2008"},{"issue":"521","key":"10.1016\/j.csda.2019.06.004_b20","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1080\/01621459.2016.1246366","article-title":"ECA: High-dimensional elliptical component analysis in non-Gaussian distributions","volume":"113","author":"Han","year":"2018","journal-title":"J. Amer. Statist. Assoc."},{"issue":"414","key":"10.1016\/j.csda.2019.06.004_b21","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1080\/01621459.1991.10475035","article-title":"Sliced inverse regression for dimension reduction","volume":"86","author":"Li","year":"1991","journal-title":"J. Amer. Statist. Assoc."},{"issue":"420","key":"10.1016\/j.csda.2019.06.004_b22","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\u2019s lemma","volume":"87","author":"Li","year":"1992","journal-title":"J. Amer. Statist. Assoc."},{"issue":"3","key":"10.1016\/j.csda.2019.06.004_b23","doi-asserted-by":"crossref","first-page":"1846","DOI":"10.1214\/12-AOS1024","article-title":"Robust rank correlation based screening","volume":"40","author":"Li","year":"2012","journal-title":"Ann. Statist."},{"issue":"479","key":"10.1016\/j.csda.2019.06.004_b24","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1198\/016214507000000536","article-title":"On directional regression for dimension reduction","volume":"102","author":"Li","year":"2007","journal-title":"J. Amer. Statist. Assoc."},{"issue":"4","key":"10.1016\/j.csda.2019.06.004_b25","doi-asserted-by":"crossref","first-page":"1580","DOI":"10.1214\/009053605000000192","article-title":"Contour regression: a general approach to dimension reduction","volume":"33","author":"Li","year":"2005","journal-title":"Ann. Statist."},{"issue":"499","key":"10.1016\/j.csda.2019.06.004_b26","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1080\/01621459.2012.695654","article-title":"Feature screening via distance correlation learning","volume":"107","author":"Li","year":"2012","journal-title":"J. Amer. Statist. Assoc."},{"issue":"5","key":"10.1016\/j.csda.2019.06.004_b27","doi-asserted-by":"crossref","first-page":"3284","DOI":"10.1214\/12-AOP803","article-title":"Distance covariance in metric spaces","volume":"41","author":"Lyons","year":"2013","journal-title":"Ann. Probab."},{"key":"10.1016\/j.csda.2019.06.004_b28","first-page":"1","article-title":"A generic sure independence screening procedure","author":"Pan","year":"2018","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/j.csda.2019.06.004_b29","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.csda.2016.11.007","article-title":"Robust estimation and variable selection in sufficient dimension reduction","volume":"108","author":"Rekabdarkolaee","year":"2017","journal-title":"Comput. Statist. Data Anal."},{"issue":"6","key":"10.1016\/j.csda.2019.06.004_b30","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1089\/106652703322756177","article-title":"Regression approaches for microarray data analysis","volume":"10","author":"Segal","year":"2003","journal-title":"J. Comput. Biol."},{"issue":"5","key":"10.1016\/j.csda.2019.06.004_b31","doi-asserted-by":"crossref","first-page":"2263","DOI":"10.1214\/13-AOS1140","article-title":"Equivalence of distance-based and RKHS-based statistics in hypothesis testing","volume":"41","author":"Sejdinovic","year":"2013","journal-title":"Ann. Statist."},{"key":"10.1016\/j.csda.2019.06.004_b32","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.jmva.2013.07.003","article-title":"Direction estimation in single-index models via distance covariance","volume":"122","author":"Sheng","year":"2013","journal-title":"J. Multivariate Anal."},{"issue":"1","key":"10.1016\/j.csda.2019.06.004_b33","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1080\/10618600.2015.1026601","article-title":"Sufficient dimension reduction via distance covariance","volume":"25","author":"Sheng","year":"2016","journal-title":"J. Comput. Graph. Statist."},{"issue":"6","key":"10.1016\/j.csda.2019.06.004_b34","doi-asserted-by":"crossref","first-page":"2769","DOI":"10.1214\/009053607000000505","article-title":"Measuring and testing dependence by correlation of distances","volume":"35","author":"Sz\u00e9kely","year":"2007","journal-title":"Ann. Statist."},{"issue":"482","key":"10.1016\/j.csda.2019.06.004_b35","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1198\/016214508000000418","article-title":"Sliced regression for dimension reduction","volume":"103","author":"Wang","year":"2008","journal-title":"J. Amer. Statist. Assoc."},{"issue":"3","key":"10.1016\/j.csda.2019.06.004_b36","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1111\/1467-9868.03411","article-title":"An adaptive estimation of dimension reduction space","volume":"64","author":"Xia","year":"2002","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"issue":"464","key":"10.1016\/j.csda.2019.06.004_b37","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. Amer. Statist. Assoc."},{"issue":"6","key":"10.1016\/j.csda.2019.06.004_b38","doi-asserted-by":"crossref","first-page":"3392","DOI":"10.1214\/11-AOS950","article-title":"Sufficient dimension reduction based on an ensemble of minimum average variance estimators","volume":"39","author":"Yin","year":"2011","journal-title":"Ann. Statist."},{"issue":"8","key":"10.1016\/j.csda.2019.06.004_b39","doi-asserted-by":"crossref","first-page":"1733","DOI":"10.1016\/j.jmva.2008.01.006","article-title":"Successive direction extraction for estimating the central subspace in a multiple-index regression","volume":"99","author":"Yin","year":"2008","journal-title":"J. Multivariate Anal."},{"issue":"1","key":"10.1016\/j.csda.2019.06.004_b40","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.jmva.2009.08.004","article-title":"An integral transform method for estimating the central mean and central subspaces","volume":"101","author":"Zeng","year":"2010","journal-title":"J. Multivariate Anal."},{"key":"10.1016\/j.csda.2019.06.004_b41","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.jmva.2014.10.006","article-title":"Robust estimating equation-based sufficient dimension reduction","volume":"134","author":"Zhou","year":"2015","journal-title":"J. Multivariate Anal."},{"issue":"474","key":"10.1016\/j.csda.2019.06.004_b42","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1198\/016214505000001285","article-title":"On sliced inverse regression with high-dimensional covariates","volume":"101","author":"Zhu","year":"2006","journal-title":"J. Amer. Statist. Assoc."},{"issue":"476","key":"10.1016\/j.csda.2019.06.004_b43","doi-asserted-by":"crossref","first-page":"1638","DOI":"10.1198\/016214506000000140","article-title":"Fourier methods for estimating the central subspace and the central mean subspace in regression","volume":"101","author":"Zhu","year":"2006","journal-title":"J. Amer. Statist. Assoc."},{"issue":"12","key":"10.1016\/j.csda.2019.06.004_b44","doi-asserted-by":"crossref","first-page":"5296","DOI":"10.1016\/j.csda.2008.05.013","article-title":"Regularized simultaneous model selection in multiple quantiles regression","volume":"52","author":"Zou","year":"2008","journal-title":"Comput. Statist. Data Anal."}],"container-title":["Computational Statistics & Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947319301380?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947319301380?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T10:01:21Z","timestamp":1759140081000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167947319301380"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12]]},"references-count":44,"alternative-id":["S0167947319301380"],"URL":"https:\/\/doi.org\/10.1016\/j.csda.2019.06.004","relation":{},"ISSN":["0167-9473"],"issn-type":[{"value":"0167-9473","type":"print"}],"subject":[],"published":{"date-parts":[[2019,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Robust sufficient dimension reduction via ball covariance","name":"articletitle","label":"Article Title"},{"value":"Computational Statistics & Data Analysis","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.csda.2019.06.004","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2019 Elsevier B.V. All rights reserved.","name":"copyright","label":"Copyright"}]}}