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2 results

  • A remark on robustness and weak continuity of M-estimators

  • Part of
  • Brenton R. Clarke
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 68 / Issue 3 / June 2000
    Published online by Cambridge University Press:
    09 April 2009, pp. 411-418
    Print publication:
    June 2000
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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.

  • Statistical expansions and locally uniform Fréchet differentiability

  • Part of
  • T. Bednarski, B. R. Clarke, W. Kolkiewicz
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 50 / Issue 1 / February 1991
    Published online by Cambridge University Press:
    09 April 2009, pp. 88-97
    Print publication:
    February 1991
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  • Estimators which have locally uniform expansions are shown in this paper to be asymptotically equivalent to M-estimators. The M-functionals corresponding to these M-estimators are seen to be locally uniformly Fréchet differentiable. Other conditions for M-functionals to be locally uniformly Fréchet differentiable are given. An example of a commonly used estimator which is robust against outliers is given to illustrate that the locally uniform expansion need not be valid.