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Bayesian nonparametric quantile regression using splines

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  • Thompson, Paul
  • Cai, Yuzhi
  • Moyeed, Rana
  • Reeve, Dominic
  • Stander, Julian
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    Abstract

    A new technique based on Bayesian quantile regression that models the dependence of a quantile of one variable on the values of another using a natural cubic spline is presented. Inference is based on the posterior density of the spline and an associated smoothing parameter and is performed by means of a Markov chain Monte Carlo algorithm. Examples of the application of the new technique to two real environmental data sets and to simulated data for which polynomial modelling is inappropriate are given. An aid for making a good choice of proposal density in the Metropolis-Hastings algorithm is discussed. The new nonparametric methodology provides more flexible modelling than the currently used Bayesian parametric quantile regression approach.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 54 (2010)
    Issue (Month): 4 (April)
    Pages: 1138-1150

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    Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:1138-1150

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    Web page: http://www.elsevier.com/locate/csda

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    1. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, April.
    2. Laurini, Fabrizio & Pauli, Francesco, 2009. "Smoothing sample extremes: The mixed model approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3842-3854, September.
    3. Wang, You-Gan & Shao, Quanxi & Zhu, Min, 2009. "Quantile regression without the curse of unsmoothness," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3696-3705, August.
    4. Athanasios Kottas & Milovan Krnjajic, 2009. "Bayesian Semiparametric Modelling in Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 36(2), pages 297-319.
    5. Lejeune, Michel G. & Sarda, Pascal, 1988. "Quantile regression: a nonparametric approach," Computational Statistics & Data Analysis, Elsevier, vol. 6(3), pages 229-239, April.
    6. Doksum, Kjell & Koo, Ja-Yong, 2000. "On spline estimators and prediction intervals in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 35(1), pages 67-82, November.
    7. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    8. Kottas A. & Gelfand A.E., 2001. "Bayesian Semiparametric Median Regression Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1458-1468, December.
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