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Robust Bayesian regression with the forward search: theory and data analysis

Author

Listed:
  • Anthony C. Atkinson

    (The London School of Economics)

  • Aldo Corbellini

    (Università di Parma)

  • Marco Riani

    (Università di Parma)

Abstract

The frequentist forward search yields a flexible and informative form of robust regression. The device of fictitious observations provides a natural way to include prior information in the search. However, this extension is not straightforward, requiring weighted regression. Bayesian versions of forward plots are used to exhibit the presence of multiple outliers in a data set from banking with 1903 observations and nine explanatory variables which shows, in this case, the clear advantages from including prior information in the forward search. Use of observation weights from frequentist robust regression is shown to provide a simple general method for robust Bayesian regression.

Suggested Citation

  • Anthony C. Atkinson & Aldo Corbellini & Marco Riani, 2017. "Robust Bayesian regression with the forward search: theory and data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 869-886, December.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:4:d:10.1007_s11749-017-0542-6
    DOI: 10.1007/s11749-017-0542-6
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    References listed on IDEAS

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    1. Riani, Marco & Perrotta, Domenico & Cerioli, Andrea, 2015. "The Forward Search for Very Large Datasets," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(c01).
    2. Marco Riani & Anthony C. Atkinson & Andrea Cerioli, 2009. "Finding an unknown number of multivariate outliers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 447-466, April.
    3. Anglin, Paul M & Gencay, Ramazan, 1996. "Semiparametric Estimation of a Hedonic Price Function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 633-648, Nov.-Dec..
    4. Anthony C. Atkinson & Marco Riani & Andrea Cerioli, 2018. "Cluster detection and clustering with random start forward searches," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(5), pages 777-798, April.
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    Cited by:

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    2. Xi Li & Runzhe Yu & Xinwei Su, 2021. "Environmental Beliefs and Pro-Environmental Behavioral Intention of an Environmentally Themed Exhibition Audience: The Mediation Role of Exhibition Attachment," SAGE Open, , vol. 11(2), pages 21582440211, June.

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    More about this item

    Keywords

    Consistency factor; Fictitious observation; Forward search; Graphical methods; Outliers; Weighted regression;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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