IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v29y2024icp189-205.html
   My bibliography  Save this article

Information Criteria for Outlier Detection Avoiding Arbitrary Significance Levels

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2452306222000107
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles
    File URL: https://libkey.io/10.1016/j.ecosta.2022.02.002?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 544-553, January.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258.
    10. 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.
    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.
    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. 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.

    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. 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.
    2. 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.
    3. Luca Greco & Giovanni Saraceno & Claudio Agostinelli, 2021. "Robust Fitting of a Wrapped Normal Model to Multivariate Circular Data and Outlier Detection," Stats, MDPI, vol. 4(2), pages 1-18, June.
    4. Brenton R. Clarke & Andrew Grose, 2023. "A further study comparing forward search multivariate outlier methods including ATLA with an application to clustering," Statistical Papers, Springer, vol. 64(2), pages 395-420, April.
    5. Silvia Salini & Andrea Cerioli & Fabrizio Laurini & Marco Riani, 2016. "Reliable Robust Regression Diagnostics," International Statistical Review, International Statistical Institute, vol. 84(1), pages 99-127, April.
    6. Andrea Cerioli & Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2018. "The power of monitoring: how to make the most of a contaminated multivariate sample," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 559-587, December.
    7. Arismendi, Juan C. & Broda, Simon, 2017. "Multivariate elliptical truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 29-44.
    8. 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.
    9. Zuppiroli, Marco & Donati, Michele & Riani, Marco & Verga, Giovanni, 2015. "The Impact of Trading Activity in Agricultural Futures Markets," 2015 Fourth Congress, June 11-12, 2015, Ancona, Italy 207848, Italian Association of Agricultural and Applied Economics (AIEAA).
    10. Anthony C. Atkinson & Andrea Cerioli & Marco Riani, 2016. "Discussion of ‘Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models’ by Johansen and Nielsen," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 349-352, June.
    11. Baishuai Zuo & Chuancun Yin & Jing Yao, 2023. "Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions," Papers 2305.09097, arXiv.org.
    12. Baishuai Zuo & Chuancun Yin, 2022. "Multivariate doubly truncated moments for generalized skew-elliptical distributions with application to multivariate tail conditional risk measures," Papers 2203.00839, arXiv.org.
    13. Greco, Luca & Pacillo, Simona & Maresca, Piera, 2023. "An impartial trimming algorithm for robust circle fitting," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    14. 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.
    15. Atkinson, Anthony C. & Riani, Marco & Torti, Francesca, 2016. "Robust methods for heteroskedastic regression," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 209-222.
    16. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2013. "Robust distances for outlier-free goodness-of-fit testing," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 29-45.
    17. Alessio Farcomeni & Luca Greco, 2015. "S-estimation of hidden Markov models," Computational Statistics, Springer, vol. 30(1), pages 57-80, March.
    18. Francesca Torti & Marco Riani & Gianluca Morelli, 2021. "Semiautomatic robust regression clustering of international trade data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 863-894, September.
    19. Claudio Agostinelli & Luca Greco, 2019. "Weighted likelihood estimation of multivariate location and scatter," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 756-784, September.
    20. Kitagawa, Toru & Muris, Chris, 2016. "Model averaging in semiparametric estimation of treatment effects," Journal of Econometrics, Elsevier, vol. 193(1), pages 271-289.

    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

    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:ecosta:v:29:y:2024:i:c:p:189-205. 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: https://www.journals.elsevier.com/econometrics-and-statistics .

    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.