Department of Economics and Business Economics

Anders Bredahl Kock

Sharp Threshold Detection Based on Sup-norm Error rates in High-dimensional Models

Research output: ResearchWorking paper

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  • rp15_10

    Submitted manuscript, 606 KB, PDF-document

  • Laurent Callot
    Laurent CallotUniversity of AmsterdamDenmark
  • Mehmet Caner
    Mehmet CanerNorth Carolina State UniversityUnited States
  • Anders Bredahl Kock
  • Juan Andres Riquelme
    Juan Andres RiquelmeNorth Carolina State UniversityUnited States
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.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages27
StatePublished - 17 Feb 2015
SeriesCREATES Research Papers
Number2015-10

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