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Original Articles

Sharp Threshold Detection Based on Sup-Norm Error Rates in High-Dimensional Models

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Pages 250-264 | Received 01 Feb 2015, Published online: 13 Mar 2017

REFERENCES

  • Akdeniz, L., Altay-Salih, A., and Caner, M. (2003), “Time Varying Betas Help in Asset Pricing: Threshold capm,” Studies in Nonlinear Dynamics and Econometrics, 6, 1–17.
  • Basci, E., and Caner, M. (2005), “Are Real Exchange Rates Non-Stationary or Non-linear? Evidence from a New Threshold Unit Root Test,” Studies in Nonlinear Dynamics and Econometrics, 9, 1–19.
  • Baum, A., Checherita-Westphal, C., and Rother, P. (2013), “Debt and Growth: New Evidence for the Euro Area,” Journal of International Money and Finance, 32, 809–821.
  • Bickel, P.J., Ritov, Y., and Tsybakov, A.B. (2009), “Simultaneous Analysis of Lasso and Dantzig Selector,” The Annals of Statistics, 1705–1732.
  • Bühlmann, P., and van De Geer, S. (2011), Statistics for High-dimensional Data: Methods, Theory and Applications, Heidelberg: Springer Science & Business Media.
  • Caner, M. (2002), “A Note on Lad Estimation of a Threshold Model,” Econometric Theory, 18, 800–814.
  • Caner, M., and Hansen, B.E. (2001), “Threshold Autoregression With a Unit Root,” Econometrica, 69, 1555–1596.
  • ——— (2004), “Iv Estimation of Threshold Models,” Econometric Theory, 20, 813–843.
  • Caner, M., Koehler-Geib, F., and Grennes, T. (2010), “Finding the Tipping Point When Sovereign Debt Turns Bad,” Sovereign Debt and Financial Crisis, 64–75.
  • Cecchetti, S.G., Mohanty, M., and Zampolli, F. (2012), “The Real Effects of Debt,” Bank for International Settlements Working Paper No. 352.
  • Eberhardt, M.M., and Presbitero, A. (2013), This Time They are Different: Heterogeneity and Nonlinearity in the Relationship Between Debt and Growth. Number 13-248. International Monetary Fund.
  • Égert, B. (2013), “The 90% Public Debt Threshold: The Rise & Fall of a Stylised Fact, working paper.
  • Friedman, J., Hastie, T., and Tibshirani, R. (2010), “Regularization Paths for Generalized Linear Models Via Coordinate Descent,” Journal of Statistical Software, 33, 1–22.
  • Hansen, B.E. (2000), “Sample Splitting and Threshold Estimation,” Econometrica, 68, 575–603.
  • ——— (1996), “Inference When a Nuisance Parameter is not Identified Under the Null Hypothesis,” Econometrica, 64, 432–430.
  • ——— (1999), “Threshold Effects in Non Dynamic Panels, Estimation, Testing and Inference,” Journal of Econometrics, 93, 345–368.
  • Hansen, B.E., and Seo, B. (2002), “Testing for Two-regime Threshold Cointegration in Vector Error Correction Models,” Journal of Econometrics, 110, 293–318.
  • Herndon, T., Ash, M., and Pollin, R. (2014), “Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff,” Cambridge Journal of Economics, 38, 257–279.
  • Horn, R., and Johnson, C. (2013), Matrix Analysis, Cambridge: Cambridge University Press.
  • Kourtellos, A., Stengos, T., and Tan, C.M. (2013), “The Effect of Public Debt on Growth in Multiple Regimes,” Journal of Macroeconomics, 38, 35–43.
  • ——— (2015), “Structural Threshold Regression,” Econometric Theory.
  • Lee, S., Seo, M.H., and Shin, Y. (2015), “The Lasso for High Dimensional Regression With a Possible Change Point,” Journal of the Royal Statistical Society, Series B.
  • Lin, T.-C. (2014), “High-Dimensional Threshold Quantile Regression With an Application to Debt Overhang and Economic Growth,” working paper, University of Wisconsin, Madison.
  • Linton, O., and Seo, M.-H. (2007), “A Smoothed Least Squares Estimator for Threshold Regression Models,” Journal of Econometrics, 141, 704–735.
  • Lounici, K. (2008), “Sup-norm Convergence Rate and Sign Concentration Property of Lasso and Dantzig Estimators,” Electronic Journal of Statistics, 2, 90–102.
  • Montgomery-Smith, S. (1993), “Comparison of Sums of Independent Identically Distributed Random Variables,” Probability and Mathematical Statistics, 14, 281–285.
  • R Development Core Team (2008), R: A Language and Environment for Statistical Computing Vienna, Austria: R Foundation for Statistical Computing.
  • Reinhart, C.M., and Rogoff, K.S. (2010), “Growth in a Time of Debt,” American Economic Review, 100, 573–78.
  • Seo, M.-H. (2006), “Bootstrap Testing for the Null of No Cointegration in a Threshold Vector Error Correction Model,” Journal of Econometrics, 134, 129–150.
  • ——— (2008), “Unit Root Test in a Threshold Autoregression: Asymptotic Theory and Residual-based Block Bootstrap,” Econometric Theory, 24, 1699–1716.
  • Geer, S., Bühlmann, P., Zhou, S., et al. (2011), “The Adaptive and the Thresholded Lasso for Potentially Misspecified Models (and a Lower Bound for the Lasso),” Electronic Journal of Statistics, 5, 688–749.
  • Geer, S.A. (2014), “Statistical Theory for High-Dimensional Models,” Lecture Notes.
  • van der Vaart, A.W., and Wellner, J.A. (1996), Weak Convergence and Empirical Processes, New York: Springer.
  • Vershynin, R. (2012), Introduction to the Non-asymptotic Analysis of Random Matrices, in Compressed Sensing: Theory and Applications, eds. Y. Eldar and G. Kutyniok, Cambridge: Cambridge University Press.
  • Xie, Y. (2014), “knitr: A Comprehensive Tool for Reproducible Research in R,” In Implementing Reproducible Computational Research. eds. V. Stodden, F. Leisch, and R. D. Peng, Chapman and Hall/CRC.

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