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Support vector quantile regression with varying coefficients

Author

Listed:
  • Jooyong Shim

    (Inje University)

  • Changha Hwang

    (Dankook University)

  • Kyungha Seok

    (Inje University)

Abstract

Quantile regression has received a great deal of attention as an important tool for modeling statistical quantities of interest other than the conditional mean. Varying coefficient models are widely used to explore dynamic patterns among popular models available to avoid the curse of dimensionality. We propose a support vector quantile regression model with varying coefficients and its two estimation methods. One uses the quadratic programming, and the other uses the iteratively reweighted least squares procedure. The proposed method can be applied easily and effectively to estimating the nonlinear regression quantiles depending on the high-dimensional vector of smoothing variables. We also present the model selection method that employs generalized cross validation and generalized approximate cross validation techniques for choosing the hyperparameters, which affect the performance of the proposed model. Numerical studies are conducted to illustrate the performance of the proposed model.

Suggested Citation

  • Jooyong Shim & Changha Hwang & Kyungha Seok, 2016. "Support vector quantile regression with varying coefficients," Computational Statistics, Springer, vol. 31(3), pages 1015-1030, September.
    • Handle: RePEc:spr:compst:v:31:y:2016:i:3:d:10.1007_s00180-016-0647-5
    DOI: 10.1007/s00180-016-0647-5
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    References listed on IDEAS

    as
    1. Shim, Jooyong & Hwang, Changha, 2009. "Support vector censored quantile regression under random censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 912-919, February.
    2. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    3. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    4. Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
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    6. 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.
    7. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    9. P. J. Heagerty & M. S. Pepe, 1999. "Semiparametric estimation of regression quantiles with application to standardizing weight for height and age in US children," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 533-551.
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