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

Yining Chen

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: change-point; minimax rate; Pointwise rate; Structural break (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 8 pages
Date: 2020-09-19
New Economics Papers: this item is included in nep-ecm and nep-ore
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Published in Biometrika, 19, September, 2020. ISSN: 0006-3444

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