Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization
Some regularization methods, including the group lasso and the adaptive group lasso, have been developed for the automatic selection of grouped variables (factors) in conditional mean regression. In many practical situations, such a problem arises naturally when a set of dummy variables is used to represent a categorical factor and/or when a set of basis functions of a continuous variable is included in the predictor set. Complementary to these earlier works, the simultaneous and automatic factor selection is examined in quantile regression. To incorporate the factor information into regularized model fitting, the adaptive sup-norm regularized quantile regression is proposed, which penalizes the empirical check loss function by the sum of factor-wise adaptive sup-norm penalties. It is shown that the proposed method possesses the oracle property. A simulation study demonstrates that the proposed method is a more appropriate tool for factor selection than the adaptive lasso regularized quantile regression.
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- repec:cup:cbooks:9780521608275 is not listed on IDEAS
- Yuan, Ming, 2006. "GACV for quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 813-829, February.
- Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
- Jinfeng Xu & Zhiliang Ying, 2010. "Simultaneous estimation and variable selection in median regression using Lasso-type penalty," Annals of the Institute of Statistical Mathematics, Springer, vol. 62(3), pages 487-514, June.
- Wang, Xiaoming & Park, Taesung & Carriere, K.C., 2010. "Variable selection via combined penalization for high-dimensional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2230-2243, October.
- Koenker R. & Geling O., 2001. "Reappraising Medfly Longevity: A Quantile Regression Survival Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 458-468, June.
- Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
- Zou, Hui & Yuan, Ming, 2008. "Regularized simultaneous model selection in multiple quantiles regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5296-5304, August.
- Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67.
- Kwon, Sunghoon & Choi, Hosik & Kim, Yongdai, 2011. "Quadratic approximation on SCAD penalized estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 421-428, January.
- Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108.
- 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.
- 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.
- 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.
- Lukas Meier & Sara van de Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71.
- repec:cup:cbooks:9780521845731 is not listed on IDEAS
- Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
- Ye, Gui-Bo & Xie, Xiaohui, 2011. "Split Bregman method for large scale fused Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1552-1569, April.
- Wang, Huixia & He, Xuming, 2007. "Detecting Differential Expressions in GeneChip Microarray Studies: A Quantile Approach," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 104-112, March.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
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