Jump or kink: note on super-efficiency in segmented linear regression break-point estimation

Chen, Yining ORCID: 0000-0003-1697-1920 (2020) Jump or kink: note on super-efficiency in segmented linear regression break-point estimation. Biometrika. ISSN 0006-3444

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Abstract

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.

Item Type:	Article
Official URL:	https://academic.oup.com/biomet
Additional Information:	© 2020 Biometrika Trust
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	19 Feb 2020 09:45
Last Modified:	12 Dec 2024 02:04
URI:	http://eprints.lse.ac.uk/id/eprint/103488

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