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

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  • Chen, Yining

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.

Suggested Citation

  • Chen, Yining, 2020. "Jump or kink: note on super-efficiency in segmented linear regression break-point estimation," LSE Research Online Documents on Economics 103488, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:103488
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    File URL: http://eprints.lse.ac.uk/103488/
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    References listed on IDEAS

    as
    1. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    2. Rafal Baranowski & Yining Chen & Piotr Fryzlewicz, 2019. "Narrowest‐over‐threshold detection of multiple change points and change‐point‐like features," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 649-672, July.
    3. Ritabrata Das & Moulinath Banerjee & Bin Nan & Huiyong Zheng, 2016. "Fast Estimation of Regression Parameters in a Broken-Stick Model for Longitudinal Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1132-1143, July.
    4. Wishart, Justin Rory, 2011. "Minimax lower bound for kink location estimators in a nonparametric regression model with long-range dependence," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1871-1875.
    5. Hidalgo, Javier & Lee, Jungyoon & Seo, Myung Hwan, 2019. "Robust inference for threshold regression models," Journal of Econometrics, Elsevier, vol. 210(2), pages 291-309.
    6. Bruce E. Hansen, 2017. "Regression Kink With an Unknown Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 228-240, April.
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    More about this item

    Keywords

    change-point; minimax rate; Pointwise rate; Structural break;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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