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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主要作者: Lian, Heng
其他作者: School of Physical and Mathematical Sciences
格式: Article
語言:English
出版: 2013
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在線閱讀:https://hdl.handle.net/10356/96500
http://hdl.handle.net/10220/11928
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機構: Nanyang Technological University
語言: English
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總結: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.