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, North Carolina State University, USA
We propose a new estimator, the thresholded scaled Lasso, in high dimensional threshold regressions. First, we establish an upper bound on the sup-norm estimation error of the scaled Lasso estimator of Lee et al. (2012). This is a non-trivial task as the literature on highdimensional models has focused almost exclusively on estimation errors in stronger norms. 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.
OriginalsprogEngelsk
UdgivelsesstedAarhus
UdgiverInstitut for Økonomi, Aarhus Universitet
Antal sider27
StatusUdgivet - 17 feb. 2015
SerietitelCREATES Research Papers
Nummer2015-10

    Forskningsområder

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

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