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Sharp Threshold Detection based on Sup-Norm Error Rates in High-dimensional Models

Listed author(s):
  • Laurent Callot

    (VU University Amsterdam, the Netherlands)

  • Mehmet Caner

    (North Carolina State University, United States)

  • Anders Bredahl Kock

    (Aarhus University, Denmark)

  • Juan Andres Riquelme

    (North Carolina State University, United States)

We propose a new estimator, the thresholded scaled Lasso, in high dimensional threshold regressions. First, we establish an upper bound on the ℓ ∞ estimation error of the scaled Lasso estimator of Lee et al. (2012). This is a non-trivial task as the literature on high-dimensional models has focused almost exclusively on ℓ 1 and ℓ 2 estimation errors. We show that this sup-norm bound can be used to distinguish between zero and non-zero coefficients at a much finer scale than would have been possible using classical oracle inequalities. Thus, our sup-norm bound is tailored to consistent variable selection via thresholding. Our simulations show that thresholding the scaled Lasso yields substantial improvements in terms of variable selection. Finally, we use our estimator to shed further empirical light on the long running debate on the relationship between the level of debt (public and private) and GDP growth.

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File URL: http://papers.tinbergen.nl/15019.pdf
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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 15-019/III.

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Date of creation: 10 Feb 2015
Handle: RePEc:tin:wpaper:20150019
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  1. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
  2. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, vol. 110(2), pages 293-318, October.
  3. Thomas Herndon & Michael Ash & Robert Pollin, 2014. "Does high public debt consistently stifle economic growth? A critique of Reinhart and Rogoff," Cambridge Journal of Economics, Oxford University Press, vol. 38(2), pages 257-279.
  4. Hansen, Bruce E., 1999. "Threshold effects in non-dynamic panels: Estimation, testing, and inference," Journal of Econometrics, Elsevier, vol. 93(2), pages 345-368, December.
  5. Carmen M. Reinhart & Kenneth S. Rogoff, 2010. "Growth in a Time of Debt," American Economic Review, American Economic Association, vol. 100(2), pages 573-578, May.
  6. Seo, Myung Hwan, 2008. "Unit Root Test In A Threshold Autoregression: Asymptotic Theory And Residual-Based Block Bootstrap," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1699-1716, December.
  7. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
  8. Baum, Anja & Checherita-Westphal, Cristina & Rother, Philipp, 2013. "Debt and growth: New evidence for the euro area," Journal of International Money and Finance, Elsevier, vol. 32(C), pages 809-821.
  9. Caner, Mehmet & Grennes,Thomas & Koehler-Geib, Fritzi, 2010. "Finding the tipping point -- when sovereign debt turns bad," Policy Research Working Paper Series 5391, The World Bank.
  10. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2016. "The lasso for high dimensional regression with a possible change point," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 193-210, 01.
  11. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  12. Basci Erdem & Caner Mehmet, 2005. "Are Real Exchange Rates Nonlinear or Nonstationary? Evidence from a New Threshold Unit Root Test," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-21, December.
  13. Seo, Myunghwan, 2006. "Bootstrap testing for the null of no cointegration in a threshold vector error correction model," Journal of Econometrics, Elsevier, vol. 134(1), pages 129-150, September.
  14. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
  15. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
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