{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,19]],"date-time":"2026-04-19T03:34:48Z","timestamp":1776569688866,"version":"3.51.2"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2020,9,19]],"date-time":"2020-09-19T00:00:00Z","timestamp":1600473600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,3,2]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We consider the problem of segmented linear regression with a single breakpoint, with the focus on estimating the location of the breakpoint. If $n$ is the sample size, we show that the global minimax convergence rate for this problem in terms of the mean absolute error is $O(n^{-1\/3})$. On the other hand, we demonstrate the construction of a super-efficient estimator that achieves the pointwise convergence rate of either $O(n^{-1})$ or $O(n^{-1\/2})$ for every fixed parameter value, depending on whether the structural change is a jump or a kink. The implications of this example and a potential remedy are discussed.<\/jats:p>","DOI":"10.1093\/biomet\/asaa049","type":"journal-article","created":{"date-parts":[[2020,6,5]],"date-time":"2020-06-05T11:23:05Z","timestamp":1591356185000},"page":"215-222","source":"Crossref","is-referenced-by-count":9,"title":["Jump or kink: on super-efficiency in segmented linear regression breakpoint estimation"],"prefix":"10.1093","volume":"108","author":[{"given":"Yining","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Statistics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, U.K"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,9,19]]},"reference":[{"key":"2021041507551743000_B1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.2307\/2998540","article-title":"Estimating and testing linear models with multiple structural changes","volume":"66","author":"Bai,","year":"1998","journal-title":"Econometrica"},{"key":"2021041507551743000_B2","doi-asserted-by":"crossref","first-page":"720","DOI":"10.1214\/17-AOS1633","article-title":"Divide and conquer in non-standard problems and the super-efficiency phenomenon","volume":"47","author":"Banerjee,","year":"2019","journal-title":"Ann. 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