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Upper and Lower Bounds for Breakdown Points

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Robustness and Complex Data Structures

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Abstract

General upper and lower bounds for the finite sample breakdown point are presented. The general upper bound is obtained by an approach of Davies and Gather using algebraic groups of transformations. It is shown that the upper bound for the finite sample breakdown point has a simpler form than for the population breakdown point. This result is applied to multivariate regression. It is shown that the upper bounds of the breakdown points of estimators of regression parameters, location and scatter can be obtained with the same group of transformations. The general lower bound for the breakdown point of some estimators is given via the concept of d-fullness introduced by Vandev. This provides that the lower bound and the upper bound can coincide for least trimmed squares estimators for multivariate regression and simultaneous estimation of scale and regression parameter.

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Author information

Authors and Affiliations

  1. Faculty of Statistics, TU Dortmund University, 44221, Dortmund, Germany

    Christine H. Müller

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  1. Christine H. Müller
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Correspondence to Christine H. Müller .

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Editors and Affiliations

  1. Halle-Wittenberg, Faculty of Law and Economics, Martin-Luther-University, Große Steinstraße 73, Halle, 06099, Germany

    Claudia Becker

  2. Faculty of Statistics, TU Dortmund University, Vogelpothsweg 87, Dortmund, 44227, Germany

    Roland Fried

  3. Faculty of Statistics, TU Dortmund University, Vogelpothsweg 87, Dortmund, 44227, Germany

    Sonja Kuhnt

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Müller, C.H. (2013). Upper and Lower Bounds for Breakdown Points. In: Becker, C., Fried, R., Kuhnt, S. (eds) Robustness and Complex Data Structures. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35494-6_5

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