Uniform asymptotics for S- and MM-regression estimators |
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Authors: | Marek Omelka Matías Salibián-Barrera |
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Institution: | 1.Department of Probability and Mathematical Statistics,Charles University,Prague,Czech Republic;2.Jaroslav Hájek Centre for Theoretical and Applied Statistics,Charles University,Prague,Czech Republic;3.Department of Statistics,The University of British Columbia,Vancouver,Canada |
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Abstract: | In this paper we find verifiable regularity conditions to ensure that S-estimators of scale and regression and MM-estimators
of regression are uniformly consistent and uniformly asymptotically normally distributed over contamination neighbourhoods.
Moreover, we show how to calculate the size of these neighbourhoods. In particular, we find that, for MM-estimators computed
with Tukey’s family of bisquare score functions, there is a trade-off between the size of these neighbourhoods and both the
breakdown point of the S-estimators and the leverage of the contamination that is allowed in the neighbourhood. These results
extend previous work of Salibian-Barrera and Zamar for location-scale to the linear regression model. |
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Keywords: | |
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