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Bayesian nonparametric quantile regression using splines


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


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.

Suggested Citation

  • Thompson, Paul & Cai, Yuzhi & Moyeed, Rana & Reeve, Dominic & Stander, Julian, 2010. "Bayesian nonparametric quantile regression using splines," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1138-1150, April.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:1138-1150

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. Laurini, Fabrizio & Pauli, Francesco, 2009. "Smoothing sample extremes: The mixed model approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3842-3854, September.
    4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, May.
    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. 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.
    7. 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.
    8. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
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    Cited by:

    1. Yuzhi Cai, 2016. "A Comparative Study Of Monotone Quantile Regression Methods For Financial Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-16, May.
    2. repec:bla:istatr:v:84:y:2016:i:3:p:327-344 is not listed on IDEAS
    3. Kostov, Philip & Davidova, Sophia & Bailey, Alastair, 2016. "Effect of family labour on output of farms in selected EU Member States: A non-parametric quantile regression approach," 90th Annual Conference, April 4-6, 2016, Warwick University, Coventry, UK 236358, Agricultural Economics Society.

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