{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,13]],"date-time":"2026-09-13T11:15:50Z","timestamp":1789298150926,"version":"build-2803163510"},"reference-count":45,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2017,9,15]],"date-time":"2017-09-15T00:00:00Z","timestamp":1505433600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100006094","name":"General University Research Program at the University of Delaware","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006094","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,3,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Modern technology often generates data with complex structures in which both response and explanatory variables are matrix valued. Existing methods in the literature can tackle matrix-valued predictors but are rather limited for matrix-valued responses. We study matrix variate regressions for such data, where the response Y on each experimental unit is a random matrix and the predictor X can be either a scalar, a vector or a matrix, treated as non-stochastic in terms of the conditional distribution Y|X. We propose models for matrix variate regressions and then develop envelope extensions of these models. Under the envelope framework, redundant variation can be eliminated in estimation and the number of parameters can be notably reduced when the matrix variate dimension is large, possibly resulting in significant gains in efficiency. The methods proposed are applicable to high dimensional settings.<\/jats:p>","DOI":"10.1111\/rssb.12247","type":"journal-article","created":{"date-parts":[[2017,9,18]],"date-time":"2017-09-18T13:56:20Z","timestamp":1505742980000},"page":"387-408","source":"Crossref","is-referenced-by-count":61,"title":["Matrix Variate Regressions and Envelope Models"],"prefix":"10.1093","volume":"80","author":[{"given":"Shanshan","family":"Ding","sequence":"first","affiliation":[{"name":"University of Delaware , Newark , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Dennis Cook","sequence":"additional","affiliation":[{"name":"University of Minnesota , Minneapolis , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,9,15]]},"reference":[{"key":"2023022002394105900_","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1111\/j.2517-6161.1995.tb02031.x","article-title":"Controlling the false discovery rate: a practical and powerful approach to multiple testing","volume":"57","author":"Benjamini","year":"1995","journal-title":"J. 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