IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v134y2019icp144-156.html
   My bibliography  Save this article

Initial robust estimation in generalized linear models

Author

Listed:
  • Agostinelli, Claudio
  • Valdora, Marina
  • Yohai, Victor J.

Abstract

Generalized Linear Models are routinely used in data analysis. Classical estimators are based on the maximum likelihood principle and it is well known that the presence of outliers can have a large impact on them. Several robust procedures have been presented in the literature, being redescending M-estimators the most widely accepted. Based on non-convex loss functions, these estimators need a robust initial estimate, which is often obtained by subsampling techniques. However, as the number of unknown parameters increases, the number of subsamples needed in order for this method to be robust, soon makes it infeasible. Furthermore the subsampling procedure provides a non deterministic starting point. A new method for computing a robust initial estimator is proposed. This method is deterministic and demands a relatively short computational time, even for large numbers of covariates. The proposed method is applied to M-estimators based on transformations. In addition, an iteratively reweighted least squares algorithm is proposed for the computation of the final estimates. The new methods are studied by means of Monte Carlo experiments.

Suggested Citation

  • Agostinelli, Claudio & Valdora, Marina & Yohai, Victor J., 2019. "Initial robust estimation in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 144-156.
    • Handle: RePEc:eee:csdana:v:134:y:2019:i:c:p:144-156
    DOI: 10.1016/j.csda.2018.12.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318302895
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.12.010?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Bergesio, Andrea & Yohai, Victor J., 2011. "Projection Estimators for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 661-671.
    2. Bianco, Ana M. & Boente, Graciela & Rodrigues, Isabel M., 2013. "Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 209-226.
    3. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, September.
    Full references (including those not matched with items on IDEAS)

    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. Bianco, Ana M. & Boente, Graciela & Rodrigues, Isabel M., 2013. "Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 209-226.
    2. Bianco, Ana M. & Martínez, Elena, 2009. "Robust testing in the logistic regression model," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4095-4105, October.
    3. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    4. Fiaschi, Davide & Giuliani, Elisa & Nieri, Federica & Salvati, Nicola, 2020. "How bad is your company? Measuring corporate wrongdoing beyond the magic of ESG metrics," Business Horizons, Elsevier, vol. 63(3), pages 287-299.
    5. Ricardo A. Maronna & Victor J. Yohai, 2021. "Optimal robust estimators for families of distributions on the integers," Statistical Papers, Springer, vol. 62(5), pages 2269-2281, October.
    6. Krichene, H. & Geiger, T. & Frieler, K. & Willner, S.N. & Sauer, I. & Otto, C., 2021. "Long-term impacts of tropical cyclones and fluvial floods on economic growth – Empirical evidence on transmission channels at different levels of development," World Development, Elsevier, vol. 144(C).
    7. Cantoni, Eva & Ronchetti, Elvezio, 2006. "A robust approach for skewed and heavy-tailed outcomes in the analysis of health care expenditures," Journal of Health Economics, Elsevier, vol. 25(2), pages 198-213, March.
    8. Stoklosa, Jakub & Huggins, Richard M., 2012. "A robust P-spline approach to closed population capture–recapture models with time dependence and heterogeneity," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 408-417.
    9. Rodriguez, Daniela & Valdora, Marina, 2019. "The breakdown point of the median of means tournament," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 108-112.
    10. Ollinger, Michael & Houser, Matthew, 2020. "Ground beef recalls and subsequent food safety performance," Food Policy, Elsevier, vol. 97(C).
    11. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Xu, Wanghong, 2019. "A novel robust approach for analysis of longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 83-95.
    12. Ghosh, Abhik & Mandal, Abhijit & Martín, Nirian & Pardo, Leandro, 2016. "Influence analysis of robust Wald-type tests," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 102-126.
    13. Linke, Yuliana Yu., 2017. "Asymptotic normality of one-step M-estimators based on non-identically distributed observations," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 216-221.
    14. Cantoni, Eva & de Luna, Xavier, 2020. "Semiparametric inference with missing data: Robustness to outliers and model misspecification," Econometrics and Statistics, Elsevier, vol. 16(C), pages 108-120.
    15. Francesco Bravo, 2020. "Robust estimation and inference for general varying coefficient models with missing observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 966-988, December.
    16. Qin, Guoyou & Bai, Yang & Zhu, Zhongyi, 2009. "Robust empirical likelihood inference for longitudinal data," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2101-2108, October.
    17. Riani, Marco & Atkinson, Anthony C., 2010. "Robust model selection with flexible trimming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3300-3312, December.
    18. Alfio Marazzi & Marina Valdora & Victor Yohai & Michael Amiguet, 2019. "A robust conditional maximum likelihood estimator for generalized linear models with a dispersion parameter," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 223-241, March.
    19. Sanjoy K. Sinha, 2019. "Robust estimation in accelerated failure time models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 52-78, January.
    20. Bellio, Ruggero, 2007. "Algorithms for bounded-influence estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2531-2541, February.

    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:csdana:v:134:y:2019:i:c:p:144-156. 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/locate/csda .

    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.