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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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    4. 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.
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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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