A note on the consistency of Schwarz’s criterion in linear quantile regression with the SCAD penalty

In this short note, we demonstrate that Schwarz’s criterion, which has been used frequently in the literature on quantile regression, is consistent in variable selection. In particular, due to the recent interest in penalized likelihood for variable selection, we also show that Schwarz’s criterion c...

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Main Author: Lian, Heng
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2013
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Online Access:https://hdl.handle.net/10356/96500
http://hdl.handle.net/10220/11928
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-965002020-03-07T12:34:42Z A note on the consistency of Schwarz’s criterion in linear quantile regression with the SCAD penalty Lian, Heng School of Physical and Mathematical Sciences DRNTU::Science::Mathematics In this short note, we demonstrate that Schwarz’s criterion, which has been used frequently in the literature on quantile regression, is consistent in variable selection. In particular, due to the recent interest in penalized likelihood for variable selection, we also show that Schwarz’s criterion consistently selects the true model combined with the SCAD-penalized estimator. Although similar results have been proved for linear regression, the results obtained here are new for quantile regression, which imposes extra technical difficulties compared to mean regression, since no closed-form solution exists. 2013-07-22T03:06:00Z 2019-12-06T19:31:31Z 2013-07-22T03:06:00Z 2019-12-06T19:31:31Z 2012 2012 Journal Article Lian, H. (2012). A note on the consistency of Schwarz’s criterion in linear quantile regression with the SCAD penalty. Statistics & Probability Letters, 82(7), 1224-1228. 0167-7152 https://hdl.handle.net/10356/96500 http://hdl.handle.net/10220/11928 10.1016/j.spl.2012.03.039 en Statistics & probability letters © 2012 Elsevier B.V.
institution Nanyang Technological University
building NTU Library
country Singapore
collection DR-NTU
language English
topic DRNTU::Science::Mathematics
spellingShingle DRNTU::Science::Mathematics
Lian, Heng
A note on the consistency of Schwarz’s criterion in linear quantile regression with the SCAD penalty
description In this short note, we demonstrate that Schwarz’s criterion, which has been used frequently in the literature on quantile regression, is consistent in variable selection. In particular, due to the recent interest in penalized likelihood for variable selection, we also show that Schwarz’s criterion consistently selects the true model combined with the SCAD-penalized estimator. Although similar results have been proved for linear regression, the results obtained here are new for quantile regression, which imposes extra technical difficulties compared to mean regression, since no closed-form solution exists.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Lian, Heng
format Article
author Lian, Heng
author_sort Lian, Heng
title A note on the consistency of Schwarz’s criterion in linear quantile regression with the SCAD penalty
title_short A note on the consistency of Schwarz’s criterion in linear quantile regression with the SCAD penalty
title_full A note on the consistency of Schwarz’s criterion in linear quantile regression with the SCAD penalty
title_fullStr A note on the consistency of Schwarz’s criterion in linear quantile regression with the SCAD penalty
title_full_unstemmed A note on the consistency of Schwarz’s criterion in linear quantile regression with the SCAD penalty
title_sort note on the consistency of schwarz’s criterion in linear quantile regression with the scad penalty
publishDate 2013
url https://hdl.handle.net/10356/96500
http://hdl.handle.net/10220/11928
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