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Uniform strong consistency of robust estimators

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  • Berrendero, José R.

Abstract

In the robustness framework, the distribution underlying the data is not totally specified and, therefore, it is convenient to use estimators whose properties hold uniformly over the whole set of possible distributions. In this paper, we give two general results on uniform strong consistency and apply them to study the uniform consistency of some classes of robust estimators over contamination neighborhoods. Some instances covered by our results are Huber's M-estimators, quantiles, or generalized S-estimators.

Suggested Citation

  • Berrendero, José R., 2003. "Uniform strong consistency of robust estimators," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 159-168, August.
    • Handle: RePEc:eee:stapro:v:64:y:2003:i:2:p:159-168
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    References listed on IDEAS

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    1. Zielinski, Ryszard, 1998. "Uniform strong consistency of sample quantiles," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 115-119, February.
    2. Hossjer, O. & Croux, C. & Rousseeuw, P. J., 1994. "Asymptotics of Generalized S-Estimators," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 148-177, October.
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    Cited by:

    1. José Berrendero & Ruben Zamar, 2006. "A note on the uniform asymptotic normality of location M-estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(1), pages 55-69, February.

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