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August 2004 Uniform asymptotics for robust location estimates when the scale is unknown
Matias Salibian-Barrera, Ruben H. Zamar
Ann. Statist. 32(4): 1434-1447 (August 2004). DOI: 10.1214/009053604000000544


Most asymptotic results for robust estimates rely on regularity conditions that are difficult to verify in practice. Moreover, these results apply to fixed distribution functions. In the robustness context the distribution of the data remains largely unspecified and hence results that hold uniformly over a set of possible distribution functions are of theoretical and practical interest. Also, it is desirable to be able to determine the size of the set of distribution functions where the uniform properties hold. In this paper we study the problem of obtaining verifiable regularity conditions that suffice to yield uniform consistency and uniform asymptotic normality for location robust estimates when the scale of the errors is unknown. We study M-location estimates calculated with an S-scale and we obtain uniform asymptotic results over contamination neighborhoods. Moreover, we show how to calculate the maximum size of the contamination neighborhoods where these uniform results hold. There is a trade-off between the size of these neighborhoods and the breakdown point of the scale estimate.


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Matias Salibian-Barrera. Ruben H. Zamar. "Uniform asymptotics for robust location estimates when the scale is unknown." Ann. Statist. 32 (4) 1434 - 1447, August 2004.


Published: August 2004
First available in Project Euclid: 4 August 2004

zbMATH: 1047.62022
MathSciNet: MR2089129
Digital Object Identifier: 10.1214/009053604000000544

Primary: 62E20 , 62F12 , 62F35

Keywords: M-estimates , robust inference , robust location and scale models , robustness

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 4 • August 2004
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