{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T12:52:39Z","timestamp":1788871959994,"version":"build-2803163510"},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,4,7]],"date-time":"2023-04-07T00:00:00Z","timestamp":1680825600000},"content-version":"vor","delay-in-days":6316,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"US National Science Foundation","doi-asserted-by":"publisher","award":["DMS 04-05360"],"award-info":[{"award-number":["DMS 04-05360"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006,2,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Sliced inverse regression is one of the widely used dimension reduction methods. Chiaromonte and co-workers extended this method to regressions with qualitative predictors and developed a method, partial sliced inverse regression, under the assumption that the covariance matrices of the continuous predictors are constant across the levels of the qualitative predictor. We extend partial sliced inverse regression by removing the restrictive homogeneous covariance condition. This extension, which significantly expands the applicability of the previous methodology, is based on a new estimation method that makes use of a non-linear least squares objective function.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2005.00534.x","type":"journal-article","created":{"date-parts":[[2005,12,21]],"date-time":"2005-12-21T06:07:16Z","timestamp":1135145236000},"page":"89-107","source":"Crossref","is-referenced-by-count":4,"title":["Sufficient Dimension Reduction in Regressions Across Heterogeneous Subpopulations"],"prefix":"10.1093","volume":"68","author":[{"given":"Liqiang","family":"Ni","sequence":"first","affiliation":[{"name":"University of Central Florida , Orlando , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Dennis Cook","sequence":"additional","affiliation":[{"name":"University of Minnesota , St Paul , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2005,12,21]]},"reference":[{"key":"2023040800102040100_","volume-title":"An Introduction to Multivariate Statistical Analysis","author":"Anderson","year":"1984"},{"key":"2023040800102040100_","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. Am. Statist. Ass."},{"key":"2023040800102040100_","first-page":"667","article-title":"Binary regressors in dimension reduction models: a new look at treatment comparisons","volume":"5","author":"Carroll","year":"1995","journal-title":"Statist. Sin."},{"key":"2023040800102040100_","first-page":"289","article-title":"Can SIR be as popular as multiple linear regression?","volume":"8","author":"Chen","year":"1998","journal-title":"Statist. Sin."},{"key":"2023040800102040100_","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1214\/aos\/1021379862","article-title":"Sufficient dimension reduction in regressions with categorical predictors","volume":"30","author":"Chiaromonte","year":"2002","journal-title":"Ann. Statist."},{"key":"2023040800102040100_","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. Am. Statist. Ass."},{"key":"2023040800102040100_","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. Am. Statist. Ass."},{"key":"2023040800102040100_","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316931","volume-title":"Regression Graphics: Ideas for Studying Regressions through Graphics","author":"Cook","year":"1998"},{"key":"2023040800102040100_","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1080\/01621459.2000.10474270","article-title":"Identifying regression outliers and mixtures graphically","volume":"95","author":"Cook","year":"2000","journal-title":"J. Am. Statist. Ass."},{"key":"2023040800102040100_","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1080\/01621459.1994.10476784","article-title":"Reweighting to achieve elliptically contoured covariates in regression","volume":"89","author":"Cook","year":"1994","journal-title":"J. Am. Statist. Ass."},{"key":"2023040800102040100_","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":"2023040800102040100_","first-page":"328","article-title":"Discussion on \u2018Sliced inverse regression for dimension reduction\u2019 (by K.-C. Li)","volume":"86","author":"Cook","year":"1991","journal-title":"J. Am. Statist. Ass."},{"key":"2023040800102040100_","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316948","volume-title":"Applied Regression including Computing and Graphics","author":"Cook","year":"1999"},{"key":"2023040800102040100_","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1080\/00949659308811484","article-title":"Tail areas of linear combinations of chi-squares and non-central chi-squares","volume":"45","author":"Field","year":"1993","journal-title":"J. Statist. Computn Simuln"},{"key":"2023040800102040100_","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1214\/aos\/1176349155","article-title":"On almost linearity of low dimensional projections from high dimensional data","volume":"21","author":"Hall","year":"1993","journal-title":"Ann. Statist."},{"key":"2023040800102040100_","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1214\/aos\/1015345954","article-title":"Structure adaptive approach for dimension reduction","volume":"29","author":"Hristache","year":"2001","journal-title":"Ann. Statist."},{"key":"2023040800102040100_","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. Statist. Ass."},{"key":"2023040800102040100_","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1002\/jae.639","article-title":"Estimating economic relationships subject to firm- and time-varying equality and inequality constraints","volume":"16","author":"O'Donnell","year":"2001","journal-title":"J. Appl. Econometr."},{"key":"2023040800102040100_","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316436","volume-title":"Linear Statistical Inference and Its Applications","author":"Rao","year":"1973","edition":"2nd"},{"key":"2023040800102040100_","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1137\/1022057","article-title":"Algorithms for separable nonlinear least squares problems","volume":"22","author":"Ruhe","year":"1980","journal-title":"SIAM Rev."},{"key":"2023040800102040100_","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1080\/01621459.1986.10478251","article-title":"Asymptotic theory of overparameterized structural models","volume":"81","author":"Shapiro","year":"1986","journal-title":"J. Am. Statist. Ass."},{"key":"2023040800102040100_","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"}],"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%2Fj.1467-9868.2005.00534.x","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/68\/1\/89\/49794821\/jrsssb_68_1_89.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/68\/1\/89\/49794821\/jrsssb_68_1_89.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T19:32:27Z","timestamp":1683315147000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/68\/1\/89\/7110645"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,12,21]]},"references-count":22,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,12,21]]},"published-print":{"date-parts":[[2006,2,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.1467-9868.2005.00534.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2006,2]]},"published":{"date-parts":[[2005,12,21]]}}}