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October 2006 Multidimensional trimming based on projection depth
Yijun Zuo
Ann. Statist. 34(5): 2211-2251 (October 2006). DOI: 10.1214/009053606000000713

Abstract

As estimators of location parameters, univariate trimmed means are well known for their robustness and efficiency. They can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy-tailed models. This paper introduces multidimensional trimmed means based on projection depth induced regions. Robustness of these depth trimmed means is investigated in terms of the influence function and finite sample breakdown point. The influence function captures the local robustness whereas the breakdown point measures the global robustness of estimators. It is found that the projection depth trimmed means are highly robust locally as well as globally. Asymptotics of the depth trimmed means are investigated via those of the directional radius of the depth induced regions. The strong consistency, asymptotic representation and limiting distribution of the depth trimmed means are obtained. Relative to the mean and other leading competitors, the depth trimmed means are highly efficient at normal or symmetric models and overwhelmingly more efficient when these models are contaminated. Simulation studies confirm the validity of the asymptotic efficiency results at finite samples.

Citation

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Yijun Zuo. "Multidimensional trimming based on projection depth." Ann. Statist. 34 (5) 2211 - 2251, October 2006. https://doi.org/10.1214/009053606000000713

Information

Published: October 2006
First available in Project Euclid: 23 January 2007

zbMATH: 1106.62057
MathSciNet: MR2291498
Digital Object Identifier: 10.1214/009053606000000713

Subjects:
Primary: 62E20
Secondary: 62G20 , 62G35

Keywords: asymptotics , Breakdown point , depth regions , directional radius , efficiency , influence function , multivariate trimmed means , projection depth , robustness

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 5 • October 2006
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