Anders Bredahl Kock

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

Publikation: Working paperForskning

Standard

Sharp Threshold Detection Based on Sup-norm Error rates in High-dimensional Models. / Callot, Laurent; Caner, Mehmet; Kock, Anders Bredahl; Riquelme, Juan Andres.

Aarhus : Institut for Økonomi, Aarhus Universitet, 2015.

Publikation: Working paperForskning

Harvard

Callot, L, Caner, M, Kock, AB & Riquelme, JA 2015 'Sharp Threshold Detection Based on Sup-norm Error rates in High-dimensional Models' Institut for Økonomi, Aarhus Universitet, Aarhus.

APA

Callot, L., Caner, M., Kock, A. B., & Riquelme, J. A. (2015). Sharp Threshold Detection Based on Sup-norm Error rates in High-dimensional Models. Institut for Økonomi, Aarhus Universitet. CREATES Research Papers Nr. 2015-10

CBE

Callot L, Caner M, Kock AB, Riquelme JA. 2015. Sharp Threshold Detection Based on Sup-norm Error rates in High-dimensional Models. Aarhus: Institut for Økonomi, Aarhus Universitet.

MLA

Callot, Laurent o.a.. Sharp Threshold Detection Based on Sup-norm Error rates in High-dimensional Models. Aarhus: Institut for Økonomi, Aarhus Universitet. (CREATES Research Papers; Journal nr. 2015-10). 2015., 27 s.

Vancouver

Callot L, Caner M, Kock AB, Riquelme JA. Sharp Threshold Detection Based on Sup-norm Error rates in High-dimensional Models. Aarhus: Institut for Økonomi, Aarhus Universitet. 2015 feb 17.

Author

Callot, Laurent ; Caner, Mehmet ; Kock, Anders Bredahl ; Riquelme, Juan Andres. / Sharp Threshold Detection Based on Sup-norm Error rates in High-dimensional Models. Aarhus : Institut for Økonomi, Aarhus Universitet, 2015. (CREATES Research Papers; Nr. 2015-10).

Bibtex

@techreport{a21f930caf5b4be187713b2926896a16,
title = "Sharp Threshold Detection Based on Sup-norm Error rates in High-dimensional Models",
abstract = "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.",
keywords = "Threshold model, sup-norm bound, thresholded scaled Lasso, oracle inequality, debt effect on GDP growth",
author = "Laurent Callot and Mehmet Caner and Kock, {Anders Bredahl} and Riquelme, {Juan Andres}",
year = "2015",
month = feb,
day = "17",
language = "English",
series = "CREATES Research Papers",
publisher = "Institut for {\O}konomi, Aarhus Universitet",
number = "2015-10",
type = "WorkingPaper",
institution = "Institut for {\O}konomi, Aarhus Universitet",

}

RIS

TY - UNPB

T1 - Sharp Threshold Detection Based on Sup-norm Error rates in High-dimensional Models

AU - Callot, Laurent

AU - Caner, Mehmet

AU - Kock, Anders Bredahl

AU - Riquelme, Juan Andres

PY - 2015/2/17

Y1 - 2015/2/17

N2 - 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.

AB - 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.

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

M3 - Working paper

T3 - CREATES Research Papers

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

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -