IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v193y2023ics0167715222002061.html

Theoretical properties of Bayesian Student-t linear regression

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715222002061
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2022.109693?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gagnon, Philippe & Wang, Yuxi, 2024. "Robust heavy-tailed versions of generalized linear models with applications in actuarial science," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    2. Hamura, Yasuyuki & Irie, Kaoru & Sugasawa, Shonosuke, 2024. "Posterior robustness with milder conditions: Contamination models revisited," Statistics & Probability Letters, Elsevier, vol. 210(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Divan A. Burger & Sean van der Merwe & Emmanuel Lesaffre & Peter C. le Roux & Morgan J. Raath‐Krüger, 2023. "A robust mixed‐effects parametric quantile regression model for continuous proportions: Quantifying the constraints to vitality in cushion plants," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(4), pages 444-470, November.
    2. Gagnon, Philippe & Wang, Yuxi, 2024. "Robust heavy-tailed versions of generalized linear models with applications in actuarial science," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    3. Heeju Lim & Victor E. Lachos & Victor H. Lachos, 2026. "Bayesian analysis of heavy-tailed Heckman selection models using Hamiltonian Monte Carlo," Computational Statistics, Springer, vol. 41(2), pages 1-34, February.
    4. Cappelen, Alexander W. & Sørensen, Erik Ø. & Tungodden, Bertil & Xu, Xiaogeng, 2025. "Risk taking on behalf of others: Does the timing of uncertainty revelation matter?," Discussion Paper Series in Economics 13/2025, Norwegian School of Economics, Department of Economics.
    5. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    6. Francis,David C. & Kubinec ,Robert, 2022. "Beyond Political Connections : A Measurement Model Approach to Estimating Firm-levelPolitical Influence in 41 Economies," Policy Research Working Paper Series 10119, The World Bank.
    7. Martinovici, A., 2019. "Revealing attention - how eye movements predict brand choice and moment of choice," Other publications TiSEM 7dca38a5-9f78-4aee-bd81-c, Tilburg University, School of Economics and Management.
    8. Yongping Bao & Ludwig Danwitz & Fabian Dvorak & Sebastian Fehrler & Lars Hornuf & Hsuan Yu Lin & Bettina von Helversen, 2022. "Similarity and Consistency in Algorithm-Guided Exploration," CESifo Working Paper Series 10188, CESifo.
    9. Torsten Heinrich & Jangho Yang & Shuanping Dai, 2020. "Growth, development, and structural change at the firm-level: The example of the PR China," Papers 2012.14503, arXiv.org.
    10. van Kesteren Erik-Jan & Bergkamp Tom, 2023. "Bayesian analysis of Formula One race results: disentangling driver skill and constructor advantage," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 19(4), pages 273-293, December.
    11. Xin Xu & Yang Lu & Yupeng Zhou & Zhiguo Fu & Yanjie Fu & Minghao Yin, 2021. "An Information-Explainable Random Walk Based Unsupervised Network Representation Learning Framework on Node Classification Tasks," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    12. Spilker Finn & Ötting Marius, 2024. "No cheering in the background? Individual performance in professional darts during COVID-19," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 20(3), pages 219-234.
    13. Xiaoyue Xi & Simon E. F. Spencer & Matthew Hall & M. Kate Grabowski & Joseph Kagaayi & Oliver Ratmann & Rakai Health Sciences Program and PANGEA‐HIV, 2022. "Inferring the sources of HIV infection in Africa from deep‐sequence data with semi‐parametric Bayesian Poisson flow models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(3), pages 517-540, June.
    14. Kuschnig, Nikolas, 2021. "Bayesian Spatial Econometrics and the Need for Software," Department of Economics Working Paper Series 318, WU Vienna University of Economics and Business.
    15. Deniz Aksoy & David Carlson, 2022. "Electoral support and militants’ targeting strategies," Journal of Peace Research, Peace Research Institute Oslo, vol. 59(2), pages 229-241, March.
    16. Luo, Nanyu & Ji, Feng & Han, Yuting & He, Jinbo & Zhang, Xiaoya, 2024. "Fitting item response theory models using deep learning computational frameworks," OSF Preprints tjxab, Center for Open Science.
    17. Richard Hunt & Shelton Peiris & Neville Weber, 2022. "Estimation methods for stationary Gegenbauer processes," Statistical Papers, Springer, vol. 63(6), pages 1707-1741, December.
    18. Antonio Parisi & B. Liseo, 2018. "Objective Bayesian analysis for the multivariate skew-t model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 277-295, June.
    19. D. Fouskakis & G. Petrakos & I. Rotous, 2020. "A Bayesian longitudinal model for quantifying students’ preferences regarding teaching quality indicators," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 255-270, August.
    20. Joseph B. Bak-Coleman & Ian Kennedy & Morgan Wack & Andrew Beers & Joseph S. Schafer & Emma S. Spiro & Kate Starbird & Jevin D. West, 2022. "Combining interventions to reduce the spread of viral misinformation," Nature Human Behaviour, Nature, vol. 6(10), pages 1372-1380, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002061. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.