{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T03:22:21Z","timestamp":1764645741830,"version":"3.37.3"},"reference-count":41,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071205"],"award-info":[{"award-number":["12071205"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computational Statistics &amp; Data Analysis"],"published-print":{"date-parts":[[2025,2]]},"DOI":"10.1016\/j.csda.2024.108052","type":"journal-article","created":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T16:27:29Z","timestamp":1725035249000},"page":"108052","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["Robust direction estimation in single-index models via cumulative divergence"],"prefix":"10.1016","volume":"202","author":[{"given":"Shuaida","family":"He","sequence":"first","affiliation":[]},{"given":"Jiarui","family":"Zhang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7444-6529","authenticated-orcid":false,"given":"Xin","family":"Chen","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.csda.2024.108052_br0010","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1007\/s10463-017-0618-9","article-title":"General rank-based estimation for regression single index models","volume":"70","author":"Bindele","year":"2018","journal-title":"Ann. Inst. Stat. Math."},{"issue":"3","key":"10.1016\/j.csda.2024.108052_br0020","doi-asserted-by":"crossref","first-page":"1204","DOI":"10.1080\/07350015.2021.1910041","article-title":"High-dimensional elliptical sliced inverse regression in non-Gaussian distributions","volume":"40","author":"Chen","year":"2022","journal-title":"J. Bus. Econ. Stat."},{"issue":"3","key":"10.1016\/j.csda.2024.108052_br0030","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1080\/10485259808832746","article-title":"A multivariate version of Kendall's \u03c4","volume":"9","author":"Choi","year":"1998","journal-title":"J. Nonparametr. Stat."},{"issue":"414","key":"10.1016\/j.csda.2024.108052_br0040","first-page":"328","article-title":"Discussion of sliced inverse regression for dimension reduction","volume":"86","author":"Cook","year":"1991","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"10.1016\/j.csda.2024.108052_br0050","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.2024.108052_br0060","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. Multivar. Anal."},{"issue":"5","key":"10.1016\/j.csda.2024.108052_br0070","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.2024.108052_br0080","doi-asserted-by":"crossref","unstructured":"Fan, Jianqing, Lv, Jinchi, 2018. Sure independence screening, Wiley StatsRef: Statistics Reference Online.","DOI":"10.1002\/9781118445112.stat08043"},{"issue":"3","key":"10.1016\/j.csda.2024.108052_br0090","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/j.spl.2011.11.025","article-title":"Rank-based inference for the single-index model","volume":"82","author":"Feng","year":"2012","journal-title":"Stat. Probab. Lett."},{"key":"10.1016\/j.csda.2024.108052_br0100","series-title":"International Conference on Algorithmic Learning Theory","first-page":"63","article-title":"Measuring statistical dependence with Hilbert-Schmidt norms","author":"Gretton","year":"2005"},{"key":"10.1016\/j.csda.2024.108052_br0110","first-page":"867","article-title":"On almost linearity of low dimensional projections from high dimensional data","author":"Hall","year":"1993","journal-title":"Ann. Stat."},{"issue":"521","key":"10.1016\/j.csda.2024.108052_br0120","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. Am. Stat. Assoc."},{"issue":"1","key":"10.1016\/j.csda.2024.108052_br0130","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1214\/aos\/1176349020","article-title":"Optimal smoothing in single-index models","volume":"21","author":"Hardle","year":"1993","journal-title":"Ann. Stat."},{"issue":"1\u20132","key":"10.1016\/j.csda.2024.108052_br0140","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0304-4076(93)90114-K","article-title":"Semiparametric least squares (sls) and weighted sls estimation of single-index models","volume":"58","author":"Ichimura","year":"1993","journal-title":"J. Econom."},{"key":"10.1016\/j.csda.2024.108052_br0150","doi-asserted-by":"crossref","unstructured":"Klock, Timo, Lanteri, Alessandro, Vigogna, Stefano, 2021. Estimating multi-index models with response-conditional least squares.","DOI":"10.1214\/20-EJS1785"},{"key":"10.1016\/j.csda.2024.108052_br0160","doi-asserted-by":"crossref","unstructured":"Kuchibhotla, Arun K., Patra, Rohit K., 2020. Efficient estimation in single index models through smoothing splines.","DOI":"10.3150\/19-BEJ1183"},{"issue":"479","key":"10.1016\/j.csda.2024.108052_br0170","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. Am. Stat. Assoc."},{"issue":"414","key":"10.1016\/j.csda.2024.108052_br0180","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. Am. Stat. Assoc."},{"issue":"499","key":"10.1016\/j.csda.2024.108052_br0190","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. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2024.108052_br0200","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1214\/17-AOS1561","article-title":"On consistency and sparsity for sliced inverse regression in high dimensions","volume":"46","author":"Lin","year":"2018","journal-title":"Ann. Stat."},{"key":"10.1016\/j.csda.2024.108052_br0210","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.jmva.2013.08.007","article-title":"A robust and efficient estimation method for single index models","volume":"122","author":"Liu","year":"2013","journal-title":"J. Multivar. Anal."},{"key":"10.1016\/j.csda.2024.108052_br0220","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.csda.2019.03.008","article-title":"Estimation for single-index models via martingale difference divergence","volume":"137","author":"Liu","year":"2019","journal-title":"Comput. Stat. Data Anal."},{"issue":"4","key":"10.1016\/j.csda.2024.108052_br0230","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/S0167-7152(98)00272-7","article-title":"Some robust estimates of principal components","volume":"43","author":"Marden","year":"1999","journal-title":"Stat. Probab. Lett."},{"key":"10.1016\/j.csda.2024.108052_br0240","series-title":"International Conference on Machine Learning","first-page":"1085","article-title":"Algorithms for direct 0\u20131 loss optimization in binary classification","author":"Nguyen","year":"2013"},{"key":"10.1016\/j.csda.2024.108052_br0250","article-title":"A generic sure independence screening procedure","author":"Pan","year":"2018","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2024.108052_br0260","article-title":"Ball covariance: a generic measure of dependence in Banach space","author":"Pan","year":"2019","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2024.108052_br0270","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.2307\/1913713","article-title":"Semiparametric estimation of index coefficients","author":"Powell","year":"1989","journal-title":"Econometrica"},{"issue":"6","key":"10.1016\/j.csda.2024.108052_br0280","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":"507","key":"10.1016\/j.csda.2024.108052_br0290","doi-asserted-by":"crossref","first-page":"1302","DOI":"10.1080\/01621459.2014.887012","article-title":"Martingale difference correlation and its use in high-dimensional variable screening","volume":"109","author":"Shao","year":"2014","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2024.108052_br0300","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. Multivar. Anal."},{"key":"10.1016\/j.csda.2024.108052_br0310","first-page":"1236","article-title":"Brownian distance covariance","author":"Sz\u00e9kely","year":"2009","journal-title":"Ann. Appl. Stat."},{"key":"10.1016\/j.csda.2024.108052_br0320","doi-asserted-by":"crossref","unstructured":"Sz\u00e9kely, G\u00e1bor J., Rizzo, Maria L., Bakirov, Nail K., 2007. Measuring and testing dependence by correlation of distances.","DOI":"10.1214\/009053607000000505"},{"key":"10.1016\/j.csda.2024.108052_br0330","doi-asserted-by":"crossref","DOI":"10.1016\/j.csda.2020.107089","article-title":"Mm algorithms for distance covariance based sufficient dimension reduction and sufficient variable selection","volume":"155","author":"Wu","year":"2021","journal-title":"Comput. Stat. Data Anal."},{"issue":"3","key":"10.1016\/j.csda.2024.108052_br0340","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":"2","key":"10.1016\/j.csda.2024.108052_br0350","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1093\/biomet\/92.2.371","article-title":"Direction estimation in single-index regressions","volume":"92","author":"Yin","year":"2005","journal-title":"Biometrika"},{"key":"10.1016\/j.csda.2024.108052_br0360","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.csda.2019.06.004","article-title":"Robust sufficient dimension reduction via ball covariance","volume":"140","author":"Zhang","year":"2019","journal-title":"Comput. Stat. Data Anal."},{"key":"10.1016\/j.csda.2024.108052_br0370","first-page":"743","article-title":"Direction estimation in single-index regressions via Hilbert-Schmidt independence criterion","author":"Zhang","year":"2015","journal-title":"Stat. Sin."},{"issue":"1","key":"10.1016\/j.csda.2024.108052_br0380","first-page":"69","article-title":"Regularized quantile regression and robust feature screening for single index models","volume":"26","author":"Zhong","year":"2016","journal-title":"Stat. Sin."},{"key":"10.1016\/j.csda.2024.108052_br0390","article-title":"Cumulative divergence revisited","volume":"51","author":"Zhou","year":"2021","journal-title":"Sci. Sin., Math."},{"issue":"531","key":"10.1016\/j.csda.2024.108052_br0400","doi-asserted-by":"crossref","first-page":"1393","DOI":"10.1080\/01621459.2019.1632078","article-title":"Model-free forward screening via cumulative divergence","volume":"115","author":"Zhou","year":"2020","journal-title":"J. Am. Stat. Assoc."},{"issue":"4","key":"10.1016\/j.csda.2024.108052_br0410","first-page":"1379","article-title":"Semiparametric quantile regression with high-dimensional covariates","volume":"22","author":"Zhu","year":"2012","journal-title":"Stat. Sin."}],"container-title":["Computational Statistics &amp; Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947324001361?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947324001361?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,11,13]],"date-time":"2024-11-13T05:21:31Z","timestamp":1731475291000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167947324001361"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2]]},"references-count":41,"alternative-id":["S0167947324001361"],"URL":"https:\/\/doi.org\/10.1016\/j.csda.2024.108052","relation":{},"ISSN":["0167-9473"],"issn-type":[{"type":"print","value":"0167-9473"}],"subject":[],"published":{"date-parts":[[2025,2]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Robust direction estimation in single-index models via cumulative divergence","name":"articletitle","label":"Article Title"},{"value":"Computational Statistics & Data Analysis","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.csda.2024.108052","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"108052"}}