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Theoretical properties of Bayesian Student-t linear regression

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  • Gagnon, Philippe
  • Hayashi, Yoshiko

Abstract

Bayesian Student-t linear regression is a common robust alternative to the normal model, but its theoretical properties are not well understood. We aim to fill some gaps by providing analyses in two different asymptotic scenarios. The results allow to precisely characterize the trade-off between robustness and efficiency controlled through the degrees of freedom (at least asymptotically).

Suggested Citation

  • Gagnon, Philippe & Hayashi, Yoshiko, 2023. "Theoretical properties of Bayesian Student-t linear regression," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002061
    DOI: 10.1016/j.spl.2022.109693
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    References listed on IDEAS

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    1. Hamura, Yasuyuki & Irie, Kaoru & Sugasawa, Shonosuke, 2022. "Log-regularly varying scale mixture of normals for robust regression," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    2. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    3. Philippe Gagnon & Mylène Bédard & Alain Desgagné, 2021. "An automatic robust Bayesian approach to principal component regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(1), pages 84-104, January.
    4. 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.
    5. Harm Jan Boonstra & Jan van den Brakel & Sumonkanti Das, 2021. "Multilevel time series modelling of mobility trends in the Netherlands for small domains," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 985-1007, July.
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    Cited by:

    1. Hamura, Yasuyuki & Irie, Kaoru & Sugasawa, Shonosuke, 2024. "Posterior robustness with milder conditions: Contamination models revisited," Statistics & Probability Letters, Elsevier, vol. 210(C).

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