Jump or kink: on super-efficiency in segmented linear regression breakpoint estimation

Yining Chen

Biometrika, 2021, vol. 108, issue 1, 215-222

Abstract: SummaryWe 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: Changepoint; Minimax rate; Pointwise rate; Structural break (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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