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Bayesian regression with B-splines under combinations of shape constraints and smoothness properties

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  • Christophe Abraham
  • Khader Khadraoui

Abstract

type="main" xml:id="stan12054-abs-0001"> In this paper, we approach the problem of shape constrained regression from a Bayesian perspective. A B-splines basis is used to model the regression function. The smoothness of the regression function is controlled by the order of the B-splines, and the shape is controlled by the shape of an associated control polygon. Controlling the shape of the control polygon reduces to some inequality constraints on the spline coefficients. Our approach enables us to take into account combinations of shape constraints and to localize each shape constraint on a given interval. The performance of our method is investigated through a simulation study. Applications to a real data sets in food industry and Global Warming are provided.

Suggested Citation

  • Christophe Abraham & Khader Khadraoui, 2015. "Bayesian regression with B-splines under combinations of shape constraints and smoothness properties," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(2), pages 150-170, May.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:2:p:150-170
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    File URL: http://hdl.handle.net/10.1111/stan.12054
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    References listed on IDEAS

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    1. J. O. Ramsay, 1998. "Estimating smooth monotone functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 365-375.
    2. Thomas S. Shively & Thomas W. Sager & Stephen G. Walker, 2009. "A Bayesian approach to non‐parametric monotone function estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 159-175, January.
    3. Brian Neelon & David B. Dunson, 2004. "Bayesian Isotonic Regression and Trend Analysis," Biometrics, The International Biometric Society, vol. 60(2), pages 398-406, June.
    4. E. Mammen & C. Thomas‐Agnan, 1999. "Smoothing Splines and Shape Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 239-252, June.
    5. Mary Meyer & Amber Hackstadt & Jennifer Hoeting, 2011. "Bayesian estimation and inference for generalised partial linear models using shape-restricted splines," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 867-884.
    6. Enrique Alvarez & Dipak Dey, 2009. "Bayesian isotonic changepoint analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 355-370, June.
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    Cited by:

    1. Silvia Montagna & Vanessa Orani & Raffaele Argiento, 2021. "Bayesian isotonic logistic regression via constrained splines: an application to estimating the serve advantage in professional tennis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 573-604, June.
    2. Khader Khadraoui & Pierre Ribereau, 2019. "Bayesian Inference with M-splines on Spectral Measure of Bivariate Extremes," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 765-788, September.

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