Abstract
In the robustness framework, the parametric model underlying the data is usually embedded in a neighborhood of other plausible distributions. Accordingly, the asymptotic properties of robust estimates should be uniform over the whole set of possible models. In this paper, we study location M-estimates calculated with a previous generalized S-scale and show that, under some regularity conditions, they are uniformly asymptotically normal over contamination neighborhoods of known size. There is a trade off between the size of the neighborhood and the breakdown point of the GS-scale, but it is possible to adjust the estimates so that they have 50% breakdown point whereas the uniform asymptotic normality is ensured over neighborhoods that contain up to 25% of contamination. Alternatively, both the breakdown point and the size of the neighborhood could be chosen to be 38%. These results represent an improvement over those obtained recently by Salibian-Barrera and Zamar (2004)
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J.R. Berrendero was Spanish supported by Grant BFM2001-0169 and Grand 06/0050/2003 (Comunidad De Madrid)
R. H. Zamar was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).
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Berrendero, J.R., Zamar, R.H. A note on the uniform asymptotic normality of location M-estimates. Metrika 63, 55–69 (2006). https://doi.org/10.1007/s00184-005-0006-y
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DOI: https://doi.org/10.1007/s00184-005-0006-y