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Bayesian Geoadditive Seemingly Unrelated Regression

Author

Listed:
  • Stefan Lang

    (University of Munich)

  • Samson B. Adebayo

    (University of Munich)

  • Ludwig Fahrmeir

    (University of Munich)

  • Winfried J. Steiner

    (University of Regensburg)

Abstract

Summary Parametric seemingly unrelated regression (SUR) models are a common tool for multivariate regression analysis when error variables are reasonably correlated, so that separate univariate analysis may result in inefficient estimates of covariate effects. A weakness of parametric models is that they require strong assumptions on the functional form of possibly nonlinear effects of metrical covariates. In this paper, we develop a Bayesian semiparametric SUR model, where the usual linear predictors are replaced by more flexible additive predictors allowing for simultaneous nonparametric estimation of such covariate effects and of spatial effects. The approach is based on appropriate smoothness priors which allow different forms and degrees of smoothness in a general framework. Inference is fully Bayesian and uses recent Markov chain Monte Carlo techniques.

Suggested Citation

  • Stefan Lang & Samson B. Adebayo & Ludwig Fahrmeir & Winfried J. Steiner, 2003. "Bayesian Geoadditive Seemingly Unrelated Regression," Computational Statistics, Springer, vol. 18(2), pages 263-292, July.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:2:d:10.1007_s001800300144
    DOI: 10.1007/s001800300144
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    References listed on IDEAS

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    1. Gamerman, Dani & Moreira, Ajax R. B. & Rue, Havard, 2003. "Space-varying regression models: specifications and simulation," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 513-533, March.
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    4. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 11-30, March.
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    Citations

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    Cited by:

    1. Anett Weber & Winfried J. Steiner & Stefan Lang, 2017. "A comparison of semiparametric and heterogeneous store sales models for optimal category pricing," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 403-445, March.
    2. Nadja Klein & Torsten Hothorn & Luisa Barbanti & Thomas Kneib, 2022. "Multivariate conditional transformation models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 116-142, March.
    3. Wolfgang A. Brunauer & Sebastian Keiler & Stefan Lang, 2010. "Cost Drivers of Operation Charges and Variation over Time: An Analysis Based on Semiparametric SUR Models," Working Papers 2010-10, Faculty of Economics and Statistics, Universität Innsbruck.
    4. Bin Zhou & Qinfeng Xu & Jinhong You, 2011. "Efficient estimation for error component seemingly unrelated nonparametric regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(1), pages 121-138, January.
    5. Hruschka, Harald, 2006. "Relevance of functional flexibility for heterogeneous sales response models: A comparison of parametric and semi-nonparametric models," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1009-1020, October.
    6. Gamerman, Dani & Moreira, Ajax R. B., 2004. "Multivariate spatial regression models," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 262-281, November.

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