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Some quantitative relationships between two types of finite sample breakdown point

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  • Zuo, Yijun

Abstract

The two versions of finite-sample breakdown points, the addition breakdown point and the replacement breakdown point, have been employed in the derivation of the breakdown points for various estimators. However, for a given estimator, frequently only the version that is convenient in the derivation is selected. The connections between the two versions have not yet been formally explored in the literature. In this paper, quantitative relationships between the two versions of the breakdown point are formally established. The result obtained allows one to obtain the ABP directly from the RBP of estimators and vice versa and thus to avoid some unnecessary, sometimes tedious, derivations of breakdown points.

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  • Zuo, Yijun, 2001. "Some quantitative relationships between two types of finite sample breakdown point," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 369-375, February.
    • Handle: RePEc:eee:stapro:v:51:y:2001:i:4:p:369-375
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    References listed on IDEAS

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    1. Chen, Z. Q., 1995. "Bounds for the Breakdown Point of the Simplicial Median," Journal of Multivariate Analysis, Elsevier, vol. 55(1), pages 1-13, October.
    2. He, Xuming & Fung, Wing K., 2000. "High Breakdown Estimation for Multiple Populations with Applications to Discriminant Analysis," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 151-162, February.
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    Cited by:

    1. Croux, Christophe & Flandre, Cécile & Haesbroeck, Gentiane, 2002. "The breakdown behavior of the maximum likelihood estimator in the logistic regression model," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 377-386, December.
    2. Van Aelst, Stefan & Rousseeuw, Peter J. & Hubert, Mia & Struyf, Anja, 2002. "The Deepest Regression Method," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 138-166, April.
    3. Zuo, Yijun, 2024. "Non-asymptotic robustness analysis of regression depth median," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    4. Gather, Ursula & Davies, P. Laurie, 2004. "Robust Statistics," Papers 2004,20, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    5. Olive, David J., 2005. "Two simple resistant regression estimators," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 809-819, June.
    6. Olive, David J., 2004. "A resistant estimator of multivariate location and dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 93-102, May.
    7. Hennig, Christian, 2008. "Dissolution point and isolation robustness: Robustness criteria for general cluster analysis methods," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1154-1176, July.

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