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Bayesian analysis of testing general hypotheses in linear models with spherically symmetric errors

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  • Min Wang

    (The University of Texas at San Antonio)

  • Keying Ye

    (The University of Texas at San Antonio)

  • Zifei Han

    (University of International Business and Economics)

Abstract

We consider Bayesian analysis for testing the general linear hypotheses in linear models with spherically symmetric errors. These error distributions not only include some of the classical linear models as special cases, but also reduce the influence of outliers and result in a robust statistical inference. Meanwhile, the design matrix is not necessarily of full rank. By appropriately modifying mixtures of g-priors for the regression coefficients under some general linear constraints, we derive closed-form Bayes factors in terms of the ratio between two Gaussian hypergeometric functions. The proposed Bayes factors rely on the data only through the modified coefficient of determinations of the two models and are shown to be independent of the error distributions, so long as they are spherically symmetric. Moreover, we establish the results of the model selection consistency with the proposed Bayes factors in the model settings with a full-rank design matrix when the number of parameters increases with the sample size. We carry out simulation studies to assess the finite sample performance of the proposed methodology. The presented results extend some existing Bayesian testing procedures in the literature.

Suggested Citation

  • Min Wang & Keying Ye & Zifei Han, 2024. "Bayesian analysis of testing general hypotheses in linear models with spherically symmetric errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(1), pages 251-270, March.
  • Handle: RePEc:spr:testjl:v:33:y:2024:i:1:d:10.1007_s11749-023-00892-9
    DOI: 10.1007/s11749-023-00892-9
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    References listed on IDEAS

    as
    1. Ley, Eduardo & Steel, Mark F.J., 2012. "Mixtures of g-priors for Bayesian model averaging with economic applications," Journal of Econometrics, Elsevier, vol. 171(2), pages 251-266.
    2. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    3. Yuzo Maruyama & William E. Strawderman, 2014. "Robust Bayesian variable selection in linear models with spherically symmetric errors," Biometrika, Biometrika Trust, vol. 101(4), pages 992-998.
    4. repec:dau:papers:123456789/4911 is not listed on IDEAS
    5. Linhan Ouyang & Shichao Zhu & Keying Ye & Chanseok Park & Min Wang, 2022. "Robust Bayesian hierarchical modeling and inference using scale mixtures of normal distributions," IISE Transactions, Taylor & Francis Journals, vol. 54(7), pages 659-671, July.
    6. Thaís C. O. Fonseca & Marco A. R. Ferreira & Helio S. Migon, 2008. "Objective Bayesian analysis for the Student-t regression model," Biometrika, Biometrika Trust, vol. 95(2), pages 325-333.
    7. Gonzalo García-Donato & Rui Paulo, 2022. "Variable Selection in the Presence of Factors: A Model Selection Perspective," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 1847-1857, October.
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