Advanced SearchSearch Tips
Quantile Regression with Non-Convex Penalty on High-Dimensions
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Quantile Regression with Non-Convex Penalty on High-Dimensions
Choi, Ho-Sik; Kim, Yong-Dai; Han, Sang-Tae; Kang, Hyun-Cheol;
  PDF(new window)
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 norm.
Quantile regression;SCAD penalty;high-dimensions;
 Cited by
Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004). Least angle regression, Annals of Statistics, 32, 407-499 crossref(new window)

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 crossref(new window)

Kim, Y., Choi, H. and Oh, H. (2008). Smoothly clipped absolute deviation on high-dimensions, Journal of the American Statistical Association, To appear crossref(new window)

Konecker, R. and Bassett, G. (1978). Regression quantiles, Econometrica, 46, 33-50 crossref(new window)

Konecker, R. and Portnoy, S. (1994). Quantile smoothing splines, Biometrika, 81, 673-680 crossref(new window)

Li, Y. and Zhu, J. (2008). $L_{1}$-norm quantile regression, Journal of Computational and Graphical Statistics, 17, 163-185 crossref(new window)

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 crossref(new window)

Schwarz, G. (1978). Estimating the dimension of a model, The Annals of Statistics, 6, 461-464 crossref(new window)

Yuan, M. (2006). GACV for quantile smoothing splines, Computational Statistics and Data Analysis, 50, 813-829 crossref(new window)

Yuille, A. and Rangarajan, A. (2003). The concave-convex procedure, Neural Computation, 15, 915-936 crossref(new window)