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Information Criteria for Outlier Detection Avoiding Arbitrary Significance Levels

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  • Riani, Marco
  • Atkinson, Anthony Curtis
  • Corbellini, Aldo
  • Farcomeni, Alessio
  • Laurini, Fabrizio

Abstract

Information criteria for model choice are extended to the detection of outliers in regression models. For deletion of observations (hard trimming) the family of models is generated by monitoring properties of the fitted models as the trimming level is varied. For soft trimming (downweighting of observations), some properties are monitored as the efficiency or breakdown point of the robust regression is varied. Least Trimmed Squares and the Forward Search are used to monitor hard trimming, with MM- and S-estimation the methods for soft trimming. Bayesian Information Criteria (BIC) for both scenarios are developed and results about their asymptotic properties provided. In agreement with the theory, simulations and data analyses show good performance for the hard trimming methods for outlier detection. Importantly, this is achieved very simply, without the need to specify either significance levels or decision rules for multiple outliers.

Suggested Citation

  • Riani, Marco & Atkinson, Anthony Curtis & Corbellini, Aldo & Farcomeni, Alessio & Laurini, Fabrizio, 2024. "Information Criteria for Outlier Detection Avoiding Arbitrary Significance Levels," Econometrics and Statistics, Elsevier, vol. 29(C), pages 189-205.
    • Handle: RePEc:eee:ecosta:v:29:y:2024:i:c:p:189-205
    DOI: 10.1016/j.ecosta.2022.02.002
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    1. Marco Riani & Andrea Cerioli & Francesca Torti, 2014. "On consistency factors and efficiency of robust S-estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 356-387, June.
    2. Anthony C. Atkinson & Marco Riani & Aldo Corbellini, 2020. "The analysis of transformations for profit‐and‐loss data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(2), pages 251-275, April.
    3. 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.
    4. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, September.
    5. Atkinson, Anthony C. & Riani, Marco & Corbellini, Aldo, 2021. "The box-cox transformation: review and extensions," LSE Research Online Documents on Economics 103537, London School of Economics and Political Science, LSE Library.
    6. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 544-553, January.
    7. Andrea Cerioli & Alessio Farcomeni & Marco Riani, 2019. "Wild adaptive trimming for robust estimation and cluster analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(1), pages 235-256, March.
    8. Francesca Torti & Aldo Corbellini & Anthony C. Atkinson, 2021. "fsdaSAS: A Package for Robust Regression for Very Large Datasets Including the Batch Forward Search," Stats, MDPI, vol. 4(2), pages 1-21, April.
    9. Riani, Marco & Atkinson, Anthony C. & Corbellini, Aldo & Perrotta, Domenico, 2020. "Robust regression with density power divergence: theory, comparisons, and data analysis," LSE Research Online Documents on Economics 103931, London School of Economics and Political Science, LSE Library.
    10. Torti, Francesca & Corbellini, Aldo & Atkinson, Anthony C., 2021. "fsdaSAS: a package for robust regression for very large datasets including the batch forward search," LSE Research Online Documents on Economics 109895, London School of Economics and Political Science, LSE Library.
    11. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2014. "Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 167-183.
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    Cited by:

    1. Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2023. "Automatic robust Box–Cox and extended Yeo–Johnson transformations in regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 75-102, March.

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    More about this item

    Keywords

    automatic data analysis; Bayesian Information Criterion (BIC); Forward Search; Least Trimmed Squares; MM-estimation; S-estimation;
    All these keywords.

    JEL classification:

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

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