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Efficient high-breakdown M-estimators of scale

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  • Croux, Christophe

Abstract

In the location model there exist M-estimators that combine a 50% breakdown point with an arbitrarily high efficiency. In this article we show that this is also the case for M-estimators of scale at normal models, although all of the well-known M-estimators of scale have a rather low efficiency there.

Suggested Citation

  • Croux, Christophe, 1994. "Efficient high-breakdown M-estimators of scale," Statistics & Probability Letters, Elsevier, vol. 19(5), pages 371-379, April.
    • Handle: RePEc:eee:stapro:v:19:y:1994:i:5:p:371-379
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    Citations

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    Cited by:

    1. 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.
    2. John Randal & Peter Thomson & Martin Lally, 2004. "Non-parametric estimation of historical volatility," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 427-440.
    3. Ben, Marta García & Martínez, Elena & Yohai, Víctor J., 2006. "Robust estimation for the multivariate linear model based on a [tau]-scale," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1600-1622, August.
    4. Boente, Graciela & Pires, Ana M. & Rodrigues, Isabel M., 2006. "General projection-pursuit estimators for the common principal components model: influence functions and Monte Carlo study," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 124-147, January.
    5. Bali, Juan Lucas & Boente, Graciela, 2015. "Influence function of projection-pursuit principal components for functional data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 173-199.
    6. Despina Dasiou & Chronis Moyssiadis, 2001. "The 50% breakdown point in simultaneous M-estimation of location and scale," Statistical Papers, Springer, vol. 42(2), pages 243-252, April.
    7. Ana M. Bianco & Paula M. Spano, 2019. "Robust inference for nonlinear regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 369-398, June.
    8. Serneels, Sven & Verdonck, Tim, 2008. "Principal component analysis for data containing outliers and missing elements," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1712-1727, January.
    9. Van Aelst, Stefan & Willems, Gert & Zamar, Ruben H., 2013. "Robust and efficient estimation of the residual scale in linear regression," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 278-296.
    10. Croux, Christophe & Ruiz-Gazen, Anne, 2005. "High breakdown estimators for principal components: the projection-pursuit approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 206-226, July.

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