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Quantile regression with an epsilon-insensitive loss in a reproducing kernel Hilbert space

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  • Park, Jinho
  • Kim, Jeankyung

Abstract

This paper proposes a method to estimate the conditional quantile function using an epsilon-insensitive loss in a reproducing kernel Hilbert space. When choosing a smoothing parameter in nonparametric frameworks, it is necessary to evaluate the complexity of the model. In this regard, we provide a simple formula for computing an effective number of parameters when implementing an epsilon-insensitive loss. We also investigate the effects of the epsilon-insensitive loss.

Suggested Citation

  • Park, Jinho & Kim, Jeankyung, 2011. "Quantile regression with an epsilon-insensitive loss in a reproducing kernel Hilbert space," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 62-70, January.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:62-70
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    References listed on IDEAS

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    1. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, January.
    2. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    3. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
    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.
    5. Yuan, Ming, 2006. "GACV for quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 813-829, February.
    6. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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    Cited by:

    1. Park, Jinho, 2017. "Solution path for quantile regression with epsilon-insensitive loss in a reproducing kernel Hilbert space," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 205-211.

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