Anders Bredahl Kock

Sharp threshold detection based on sup-norm error rates in high-dimensional models

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  • Laurent Callot, University of Amsterdam, Danmark
  • Mehmet Caner, North Carolina State University, USA
  • Anders Bredahl Kock
  • Juan Andres Riquelme, University of Talca, Chile

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, Seo, and Shin. This is a nontrivial 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 nonzero 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. Supplementary materials for this article are available online.

TidsskriftJournal of Business and Economic Statistics
Sider (fra-til)250-264
Antal sider15
StatusUdgivet - 2017


  • Threshold model, sup-norm bound, thresholded scaled Lasso, oracle inequality, debt effect on GDP growth

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