Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization
AbstractSome 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 56 (2012)
Issue (Month): 4 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/csda
Factor selection; Linear programming; Quantile regression; Regularization; Sup-norm;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521608275, October.
- 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.
- 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.
- 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.
- 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.
- 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, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
- 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.
- 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.
- Yuan, Ming, 2006. "GACV for quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 813-829, February.
- 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.
- 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.
- 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, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
- 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.
- 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.
- 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.
- Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
- Y. Andriyana & I. Gijbels & A. Verhasselt, 2014. "P-splines quantile regression estimation in varying coefficient models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 23(1), pages 153-194, March.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.