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

详细信息	查看全文 | 推荐本文 |

• 作者：Heng Lian ; ^{henglian@ntu.edu.sg}
• 关键词：Bayesian information criterion (BIC) ; Quantile regression ; SCAD penalty ; Schwarz information criterion (SIC)
• 刊名：Statistics and Probability Letters
• 出版年：2012
• 期刊代码：56_01677152
• 类别：mt
• 出版时间：July, 2012
• 卷：82
• 期：7
• 页码：1224-1228
• 文件大小：196 K

摘要

In this short note, we demonstrate that Schwarz鈥檚 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鈥檚 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.