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A remark on robustness and weak continuity of M-estimators

Part of: Distribution theory Nonparametric inference

Published online by Cambridge University Press:  09 April 2009

Brenton R. Clarke
Brenton R. Clarke
Affiliation:
Mathematics and Statistics Division of Science and Engineering Murdoch UniversityMurdoch, WA 6150Australia e-mail: [email protected]
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Abstract

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Global weak continuity of M-functionals in a neighbourhood of the parametric distribution is established. This has implications for robustness of M-estimators vis a vis definitions put forward by Hampel. For instance the Tukey bisquare location estimator is robust on neighbourhoods of the parametric model, but the median is not.

Keywords

M-functionalsProhorov metric distanceweak continuity

MSC classification

Secondary: 62G35: Robustness 62E20: Asymptotic distribution theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 3 , June 2000 , pp. 411 - 418
Copyright
Copyright © Australian Mathematical Society 2000

References

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