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A remark on robustness and weak continuity of M-estimators

Clarke, B.R. (2000) A remark on robustness and weak continuity of M-estimators. Journal of the Australian Mathematical Society (Series A), 68 (03). pp. 411-418.

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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.

Publication Type: Journal Article
Murdoch Affiliation: School of Chemical and Mathematical Science
Publisher: Cambridge University Press
Copyright: Copyright © Australian Mathematical Society 2000
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