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

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Original languageEnglish
Pages (from-to)1224-1228
Journal / PublicationStatistics and Probability Letters
Issue number7
Publication statusPublished - Jul 2012
Externally publishedYes


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. © 2012 Elsevier B.V.

Research Area(s)

  • Bayesian information criterion (BIC), Quantile regression, SCAD penalty, Schwarz information criterion (SIC)