{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,28]],"date-time":"2026-08-28T01:30:22Z","timestamp":1787880622518,"version":"build-2784847793"},"reference-count":43,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T00:00:00Z","timestamp":1751414400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["12131006, 12222117"],"award-info":[{"award-number":["12131006, 12222117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,2,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>A bottleneck of sufficient dimension reduction (SDR) in the modern era is that, among numerous methods, only sliced inverse regression (SIR) is generally applicable in high-dimensional settings. The higher-order inverse regression methods, which form a major family of SDR methods superior to SIR at the population level, suffer from the dimensionality of their intermediate matrix-valued parameters which have excessive columns. In this paper, we propose to use a small subset of columns of the matrix-valued parameter for SDR estimation, which breaks the convention of using the ambient matrix in the higher-order inverse regression methods. With a quick column selection procedure, we then generalize these methods and their ensembles in high-dimensional sparse settings, in a uniform manner that resembles sparse SIR without additional assumptions. This is the first promising attempt in the literature to free the higher-order inverse regression methods from their dimensionality, thereby facilitating the application of SDR. Some numerical illustrations, including both simulation studies and a real data example, are provided at the end.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkaf038","type":"journal-article","created":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T07:21:35Z","timestamp":1749453695000},"page":"23-42","source":"Crossref","is-referenced-by-count":2,"title":["A unified generalization of the inverse regression methods via column selection"],"prefix":"10.1093","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-6358-7789","authenticated-orcid":false,"given":"Yin","family":"Jin","sequence":"first","affiliation":[{"name":"Center for Data Science, Zhejiang University , Hangzhou, Zhejiang 310058 ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9154-0827","authenticated-orcid":false,"given":"Wei","family":"Luo","sequence":"additional","affiliation":[{"name":"Center for Data Science, Zhejiang University , Hangzhou, 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