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 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.
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Volume (Year): 82 (2012)
Issue (Month): 7 ()
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- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007.
"Quantile And Probability Curves Without Crossing,"
Boston University - Department of Economics - Working Papers Series
WP2007-011, Boston University - Department of Economics.
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves without Crossing," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Quantile and probability curves without crossing," CeMMAP working papers CWP10/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
- Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
- Horowitz, Joel L. & Lee, Sokbae, 2005.
"Nonparametric Estimation of an Additive Quantile Regression Model,"
Journal of the American Statistical Association,
American Statistical Association, vol. 100, pages 1238-1249, December.
- Sokbae Lee & Joel L. Horowitz, 2004. "Nonparametric Estimation of an Additive Quantile Regression Model," Econometric Society 2004 Far Eastern Meetings 721, Econometric Society.
- Joel Horowitz & Sokbae Lee, 2004. "Nonparametric estimation of an additive quantile regression model," CeMMAP working papers CWP07/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- De Gooijer J.G. & Zerom D., 2003. "On Additive Conditional Quantiles With High Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 135-146, January.
- Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
- Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
- Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683.
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