{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T13:55:15Z","timestamp":1769694915979,"version":"3.49.0"},"reference-count":11,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T00:00:00Z","timestamp":1729123200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,1,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the errors. We depart from existing literature by showing that with random regressors, linear regression inference is robust to correlated errors with unknown correlation structure. The existing theoretical analyses for linear regression are no longer valid because even the asymptotic normality of the least squares coefficients breaks down in this regime. We first prove the asymptotic normality of the t statistics by establishing their Berry\u2013Esseen bounds based on a novel probabilistic analysis of self-normalized statistics. We then study the local power of the corresponding t tests and show that, perhaps surprisingly, error correlation can even enhance power in the regime of weak signals. Overall, our results show that linear regression is applicable more broadly than the conventional theory suggests, and they further demonstrate the value of randomization for ensuring robustness of inference.<\/jats:p>","DOI":"10.1093\/biomet\/asae054","type":"journal-article","created":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T16:52:38Z","timestamp":1729183958000},"source":"Crossref","is-referenced-by-count":3,"title":["With random regressors, least squares inference is robust to correlated errors with unknown correlation structure"],"prefix":"10.1093","volume":"112","author":[{"given":"Zifeng","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Statistics, Colorado State University , Fort Collins , Colorado 80523, U.S.A. zifeng.zhang@colostate.edu"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2704-2353","authenticated-orcid":false,"given":"Peng","family":"Ding","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California , Berkeley, 425 Evans Hall , Berkeley, California 94720, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, School of Global Public Health, New York University , 708 Broadway , New York, New York 10003, U.S.A. w.zhou@nyu.edu"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haonan","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Statistics, Colorado State University , Fort Collins , Colorado 80523, U.S.A. wanghn@stat.colostate.edu"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,10,17]]},"reference":[{"key":"2025012017215531600_asae054-B1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/qje\/qjac038","article-title":"When should you adjust standard errors for clustering?","volume":"138","author":"Abadie","year":"2023","journal-title":"Q. 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