{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T08:43:30Z","timestamp":1790412210079,"version":"4.1.0"},"reference-count":35,"publisher":"Oxford University Press (OUP)","issue":"3","funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly used reduced-rank methods are sensitive to data corruption, as the low-rank dependence structure between response variables and predictors is easily distorted by outliers. We propose a robust reduced-rank regression approach for joint modelling and outlier detection. The problem is formulated as a regularized multivariate regression with a sparse mean-shift parameterization, which generalizes and unifies some popular robust multivariate methods. An efficient thresholding-based iterative procedure is developed for optimization. We show that the algorithm is guaranteed to converge and that the coordinatewise minimum point produced is statistically accurate under regularity conditions. Our theoretical investigations focus on non-asymptotic robust analysis, demonstrating that joint rank reduction and outlier detection leads to improved prediction accuracy. In particular, we show that redescending \u03c8-functions can essentially attain the minimax optimal error rate, and in some less challenging problems convex regularization guarantees the same low error rate. The performance of the proposed method is examined through simulation studies and real-data examples.<\/jats:p>","DOI":"10.1093\/biomet\/asx032","type":"journal-article","created":{"date-parts":[[2017,5,11]],"date-time":"2017-05-11T20:55:52Z","timestamp":1494536152000},"page":"633-647","source":"Crossref","is-referenced-by-count":57,"title":["Robust reduced-rank regression"],"prefix":"10.1093","volume":"104","author":[{"given":"Y.","family":"She","sequence":"first","affiliation":[{"name":"Department of Statistics, Florida State University, 117 N. Woodward Avenue, Tallahassee, Florida 32306, U.S.A yshe@stat.fsu.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"K.","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Connecticut, 215 Glenbrook Road U-4120, Storrs, Connecticut 06269, U.S.A. kun.chen@uconn.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,7,12]]},"reference":[{"key":"2019071815501955700_B1","first-page":"981","article-title":"Multivariate regression S-estimators for robust estimation and inference.","volume":"15","author":"Aelst","year":"2005","journal-title":"Statist. Sinica"},{"key":"2019071815501955700_B2","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1214\/12-AOS1000","article-title":"Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions.","volume":"40","author":"Agarwal","year":"2012","journal-title":"Ann. 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