445
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

General composite quantile regression: Theory and methods

, &
Pages 2217-2236 | Received 20 Jun 2018, Accepted 21 Dec 2018, Published online: 20 Feb 2019

References

  • Fan, J., and R. Li. 2001. Variable selection via nonconvave penalized likelihood and its oracle properties. Publications of the American Statistical Association 96 (456):1348–60. doi: 10.1198/016214501753382273.
  • Hunter, D., and K. Lange. 2000. Quantile regression via an mm algorithm. Journal of Computational & Graphical Statistics 9 (1):60–77. doi: 10.2307/1390613.
  • Jiang, R., and W. Qian. 2013. Composite quantile regression for nonparametric model with random censored data. Open Journal of Statistics 3 (2):65–73. doi: 10.4236/ojs.2013.32009.
  • Jiang, X., J. Jiang, and X. Song. 2012. Oracle model selection for nonlinear models based on weighted composite quantile regression. Statistica Sinica 22 (4):1479–506.
  • Kai, B., R. Li, and H. Zou. 2010. Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72 (1):49–69. doi: 10.1111/j.1467-9868.2009.00725.x.
  • Koenker, R. 2005. Quantile regression. London: Cambridge University Press.
  • Koenker, R., and G. Bassett. 1978. Regression quantiles. Econometrica 46 (1):33–50. doi: 10.2307/1913643.
  • Koenker, R., and J. F. Machado. 1999. Goodness of fit and related inference processes for quantile regression. Publications of the American Statistical Association 94 (448):1296–310. doi: 10.1080/01621459.1999.10473882.
  • Koenker, R., P. Ng, and S. Portnoy. 1994. Quantile smoothing splines. Biometrika 81 (4):673–80. doi: 10.1093/biomet/81.4.673.
  • Kozumi, H., and G. Kobayashi. 2011. Gibbs sampling methods for bayesian quantile regression. Journal of Statistical Computation & Simulation 81 (11):1565–78. doi: 10.1080/00949655.2010.496117.
  • Nierenberg, D. W., T. A. Stukel, J. A. Baron, B. J. Dain, and E. R. Greenberg. 1989. Determinants of plasma levels of beta-carotene and retinol. skin cancer prevention study group. American Journal of Epidemiology 130 (3):511. doi: 10.1093/oxfordjournals.aje.a115365.
  • Parzen, E. 1979. Nonparametric statistical data modeling. Publications of the American Statistical Association 74 (365):105–21. doi: 10.1080/01621459.1979.10481621.
  • Sun, J., Y. Gai, and L. Lin. 2013. Weighted local linear composite quantile estimation for the case of general error distributions. Journal of Statistical Planning & Inference 143 (6):1049–63. doi: 10.1016/j.jspi.2013.01.002.
  • Tian, M. 2006. A quantile regression analysis of family background factor effects on mathematical achievement. Journal of Data Science 4 (4):461–78.
  • Tian, M., and G. Chen. 2006. Hierarchical linear regression models for conditional quantiles. Science in China Series A: Mathematics 49 (12):1800–15. doi: 10.1007/s11425-006-2023-3.
  • Tian, Y., M. Tian, and Q. Zhu. 2014. Linear quantile regression based on em algorithm. Communications in Statistics 43 (16):3464–84. doi: 10.1080/03610926.2013.766339.
  • Tibshirani, R. 1996. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological) 1996:267–88. doi: 10.1111/j.2517-6161.1996.tb02080.x.
  • Tsionas, E. G. 2003. Bayesian quantile inference. Journal of Statistical Computation & Simulation 73 (9):659–74. doi: 10.1080/0094965031000064463.
  • Tukey, J. W. 1965. Which part of the sample contains the information? Proceedings of the National Academy of Sciences of the United States of America 53 (1):127. doi: 10.1073/pnas.53.1.127.
  • Wang, H., G. Li, and G. Jiang. 2007. Robust regression shrinkage and consistent variable selection through the LAD-Lasso. Journal of Business & Economic Statistics 25 (3):347–55. doi: 10.1198/073500106000000251.
  • Yu, K., and R. A. Moye. 2008. Bayesian quantile regression. Statistics & Probability Letters 54 (4):437–47. doi: 10.1016/S0167-7152(01)00124-9.
  • Zhang, C. H. 2010. Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics 38 (2):894–942. doi: 10.1214/09-AOS729.
  • Zou, H., and M. Yuan. 2008. Composite quantile regression and the oracle model selection theory. The Annals of Statistics 36 (3):1108–26. doi: 10.1214/07-AOS507.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.