Journal
STATISTICS & PROBABILITY LETTERS
Volume 82, Issue 7, Pages 1224-1228Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.spl.2012.03.039
Keywords
Bayesian information criterion (BIC); Quantile regression; SCAD penalty; Schwarz information criterion (SIC)
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Funding
- Singapore Ministry of Education
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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. (C) 2012 Elsevier B.V. All rights reserved.
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