Browse > Article
http://dx.doi.org/10.5351/CKSS.2009.16.1.209

Quantile Regression with Non-Convex Penalty on High-Dimensions  

Choi, Ho-Sik (Dept. of Informational Statistics and Institute of Basic Science, Hoseo Univ.)
Kim, Yong-Dai (Dept. of Statistics, Seoul National Univ.)
Han, Sang-Tae (Dept. of Informational Statistics, Hoseo Univ.)
Kang, Hyun-Cheol (Dept. of Informational Statistics, Hoseo Univ.)
Publication Information
Communications for Statistical Applications and Methods / v.16, no.1, 2009 , pp. 209-215 More about this Journal
Abstract
In regression problem, the SCAD estimator proposed by Fan and Li (2001), has many desirable property such as continuity, sparsity and unbiasedness. In this paper, we extend SCAD penalized regression framework to quantile regression and hence, we propose new SCAD penalized quantile estimator on high-dimensions and also present an efficient algorithm. From the simulation and real data set, the proposed estimator performs better than quantile regression estimator with $L_1$ norm.
Keywords
Quantile regression; SCAD penalty; high-dimensions;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Yuan, M. (2006). GACV for quantile smoothing splines, Computational Statistics and Data Analysis, 50, 813-829   DOI   ScienceOn
2 Yuille, A. and Rangarajan, A. (2003). The concave-convex procedure, Neural Computation, 15, 915-936   DOI   ScienceOn
3 Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004). Least angle regression, Annals of Statistics, 32, 407-499   DOI
4 Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle prop-erties, Journal of the American Statistical Association, 96, 1348-1360   DOI   ScienceOn
5 Kim, Y., Choi, H. and Oh, H. (2008). Smoothly clipped absolute deviation on high-dimensions, Journal of the American Statistical Association, To appear   DOI   ScienceOn
6 Konecker, R. and Bassett, G. (1978). Regression quantiles, Econometrica, 46, 33-50   DOI   ScienceOn
7 Schwarz, G. (1978). Estimating the dimension of a model, The Annals of Statistics, 6, 461-464   DOI   ScienceOn
8 Konecker, R. and Portnoy, S. (1994). Quantile smoothing splines, Biometrika, 81, 673-680   DOI   ScienceOn
9 Li, Y. and Zhu, J. (2008). $L_{1}$-norm quantile regression, Journal of Computational and Graphical Statistics, 17, 163-185   DOI   ScienceOn
10 Scheetz, T. E., Kim, K. Y., Swiderski, R. E., Philp, A. R., Braun, T. A., Knudtson, K. L., Dorrance, A. M., DiBona, G. F., Huang, J., Casavant, T. L., Sheffield, V. C. and Stone, E. M. (2006). Reg-ulation of gene expression in the Mammalian eye and its relevance to eye disease, Proceedings of the National Academy of Sciences, 103, 14429-14434   DOI   ScienceOn