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On consistency factors and efficiency of robust S-estimators

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  • Marco Riani
  • Andrea Cerioli
  • Francesca Torti

Abstract

We tackle the problem of obtaining the consistency factors of robust S-estimators of location and scale both in regression and multivariate analysis. We provide theoretical results, proving new formulae for their calculation and shedding light on the relationship between these factors and important statistical properties of S-estimators. We also give computational advances, suggesting efficient procedures so that hardly any time is lost for their calculation when computing S-estimates. In addition, when the purpose is to fix the efficiency of the scale estimator, we are able to quantify to what extent the approximate algorithms which are currently available provide an acceptable solution, and when it is necessary to resort to the exact formulae. Finally, even if this paper concentrates on S-estimates and Tukey’s Biweight and optimal loss functions, the main results can be easily extended to calculate the tuning consistency factors for other popular loss function and other robust estimators. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:23:y:2014:i:2:p:356-387
    DOI: 10.1007/s11749-014-0357-7
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    References listed on IDEAS

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    1. Van Aelst, Stefan & Willems, Gert, 2011. "Robust and Efficient One-Way MANOVA Tests," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 706-718.
    2. Pavel Čížek, 2013. "Reweighted least trimmed squares: an alternative to one-step estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 514-533, September.
    3. Salibian-Barrera, Matias & Van Aelst, Stefan & Willems, Gert, 2006. "Principal Components Analysis Based on Multivariate MM Estimators With Fast and Robust Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1198-1211, September.
    4. Catherine Dehon & Marjorie Gassner & Vincenzo Verardi, 2011. "Extending the Hausman Test to Check for the presence of Outliers," Working Papers ECARES ECARES 2011-036, ULB -- Universite Libre de Bruxelles.
    5. Christophe Croux & Catherine Dehon & Abdelilah Yadine, 2011. "On the Optimality of Multivariate S‐Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(2), pages 332-341, June.
    6. 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).
    7. 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.
    8. Sonja Rieder, 2012. "Robust parameter estimation for the Ornstein–Uhlenbeck process," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 411-436, November.
    9. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    10. Cerioli, Andrea, 2010. "Multivariate Outlier Detection With High-Breakdown Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 147-156.
    11. Todorov, Valentin & Filzmoser, Peter, 2009. "An Object-Oriented Framework for Robust Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i03).
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    Cited by:

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    3. 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.
    4. 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.
    5. 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.
    6. Jack Jewson & David Rossell, 2022. "General Bayesian loss function selection and the use of improper models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1640-1665, November.
    7. Grossi, Luigi & Nan, Fany, 2019. "Robust forecasting of electricity prices: Simulations, models and the impact of renewable sources," Technological Forecasting and Social Change, Elsevier, vol. 141(C), pages 305-318.
    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. Greco, Luca & Pacillo, Simona & Maresca, Piera, 2023. "An impartial trimming algorithm for robust circle fitting," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    10. Valentin Todorov, 2018. "Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 631-639, December.

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