Open Access
December 2002 The influence function and maximum bias of Tukey's median
Zhiqiang Chen, David E. Tyler
Ann. Statist. 30(6): 1737-1759 (December 2002). DOI: 10.1214/aos/1043351255


Tukey's median is among one of the earliest known high breakdown point multivariate location statistics. Aside from its breakdown point, though, little else appears to be known about its robustness properties. In this paper we investigate other aspects of Tukey's median, and in particular we derive and study its influence function and its maximum contamination bias function. When judged by these other robustness criteria, Tukey's median again proves to be highly robust.


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Zhiqiang Chen. David E. Tyler. "The influence function and maximum bias of Tukey's median." Ann. Statist. 30 (6) 1737 - 1759, December 2002.


Published: December 2002
First available in Project Euclid: 23 January 2003

zbMATH: 1015.62058
MathSciNet: MR1969448
Digital Object Identifier: 10.1214/aos/1043351255

Primary: 62G05 , 62G20
Secondary: 62G09 , 62G10 , 62H12

Keywords: Contamination bias , contamination sensitivity , gross error sensitivity , halfspace depth , halfspace median , influence function , multivariate function , robustness , Tukey's depth

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 6 • December 2002
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