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A remark on robustness and weak continuity of M-estimators

Published online by Cambridge University Press:  09 April 2009

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

References

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