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

Laurent Callot (), Mehmet Caner (), Anders Kock and Juan Andres Riquelme
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Juan Andres Riquelme: North Carolina State University, United States

No 15-019/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: 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.

Keywords: Threshold model; sup-norm bound; thresholded scaled Lasso; oracle inequality; debt effect on gdp growth (search for similar items in EconPapers)
JEL-codes: C13 C23 C26 (search for similar items in EconPapers)
Date: 2015-02-10
New Economics Papers: this item is included in nep-ecm
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Journal Article: Sharp Threshold Detection Based on Sup-Norm Error Rates in High-Dimensional Models (2017) Downloads
Working Paper: Sharp Threshold Detection Based on Sup-norm Error rates in High-dimensional Models (2015) Downloads
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