Skip to main content
SpringerLink
Log in

Variable selection in quantile regression when the models have autoregressive errors

  • Published:
Journal of the Korean Statistical Society Aims and scope Submit manuscript

Abstract

This paper considers a problem of variable selection in quantile regression with autoregressive errors. Recently, Wu and Liu (2009) investigated the oracle properties of the SCAD and adaptive-LASSO penalized quantile regressions under non identical but independent error assumption. We further relax the error assumptions so that the regression model can hold autoregressive errors, and then investigate theoretical properties for our proposed penalized quantile estimators under the relaxed assumption. Optimizing the objective function is often challenging because both quantile loss and penalty functions may be non-differentiable and/or non-concave. We adopt the concept of pseudo data by Oh et al. (2007) to implement a practical algorithm for the quantile estimate. In addition, we discuss the convergence property ofthe proposed algorithm. The performance ofthe proposed method is compared with those of the majorization-minimization algorithm (Hunter and Li, 2005) and the difference convex algorithm (Wu and Liu, 2009) through numerical and real examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Antoniadis, A., & Fan, J. (2001). Regularization of wavelet approximations. Journal of the American Statistical Association, 96, 96–939.

    Article  MathSciNet  Google Scholar 

  • Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96, 96–1348.

    MathSciNet  MATH  Google Scholar 

  • Hunter, D. R., & Li, R. (2005). Variable selection using MM algorithms. The Annals of Statistics, 33, 33–1617.

    Article  MathSciNet  Google Scholar 

  • Knight, K. (1998). Limiting distributions for L1 regression estimators under general conditions. Annals of Statistics, 26, 26–755.

    Google Scholar 

  • Koenker, R. (2005). Quantile regression. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Koenker, R., & Xiao, Z. (2006). Quantile autoregression. Journal of the American Statistical Association, 475, 475–980.

    MathSciNet  MATH  Google Scholar 

  • Nardi, Y., & Rinaldo, A. (2011). Autoregressive process modeling via the Lasso procedure. Journal of Multivariate Analysis, 102(3), 528–549.

    Article  MathSciNet  Google Scholar 

  • Neftci, S. (1984). Are economic time series asymmetric over the business cycle? Journal of Political Economy, 92, 92–307.

    Article  Google Scholar 

  • Oh, H.-S., Lee, T. C. M., & Nychka, D. W. (2011). Fast nonparametric quantile regression with arbitrary smoothing methods. Journal of Computational and Graphical Statistics, 20, 20–510.

    MathSciNet  Google Scholar 

  • Oh, H.-S., Nychka, D. W.,& Lee, T. C. M.(2007). The role of pseudo data for robust smoothing with applicationtowavelet regression. Biometrika, 94, 94–893..

    Article  Google Scholar 

  • Pollard, D. (1991). Asymptotics for least absolute deviation regression estimators. Econometric Theory, 7, 7–186.

    Article  MathSciNet  Google Scholar 

  • Ramanathan, R. (1998). Introductory econometrics with applications. Fort Worth: Harcourt Brace College Publishers.

    Google Scholar 

  • Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society Series B, 58, 58–267.

    MathSciNet  MATH  Google Scholar 

  • Tsay, R. S. (1984). Regression models with time series errors. Journal of the American Statistical Association, 79, 79–118.

    MathSciNet  MATH  Google Scholar 

  • Wang, H., Li, G., & Tsai, C. (2007). Regression coefficient and autoregressive order shrinkage and selection via the Lasso. Journal of the Royal Statistical Society Series B, 69, 69–63.

    MathSciNet  Google Scholar 

  • Wu, Z. (2012). A note on the monotonicity of the ES-algorithm. Journal of Statistical Computation and Simulation, 82(5), 759–761.

    Article  MathSciNet  Google Scholar 

  • Wu, Y., & Liu, Y. (2009). Variable selection in quantile regression. Statistica Sinica, 19, 19–801.

    MathSciNet  MATH  Google Scholar 

  • Yoon, Y.-J., Park, C., & Lee, T. (2013). Penalized regression models with autoregressive error terms. Journal of Statistical Computation and Simulation, 83(9), 1756–1772.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Seoul National University, Seoul, 151-747, Republic of Korea

    Yaeji Lim & Hee-Seok Oh

Authors
  1. Yaeji Lim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hee-Seok Oh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yaeji Lim.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lim, Y., Oh, HS. Variable selection in quantile regression when the models have autoregressive errors. J. Korean Stat. Soc. 43, 513–530 (2014). https://doi.org/10.1016/j.jkss.2014.07.002

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/j.jkss.2014.07.002

Keywords

AMS 2000 subject classifications

Search

Navigation