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June 2006 Addendum to the discussion of “Breakdown and groups”
P. Laurie Davies, Ursula Gather
Ann. Statist. 34(3): 1577-1579 (June 2006). DOI: 10.1214/009053606000000399

Abstract

In his discussion of Davies and Gather [Ann. Statist. 33 (2005) 977–1035] Tyler pointed out that the theory developed there could not be applied to the case of directional data. He related the breakdown of directional functionals to the problem of definability. In this addendum we provide a concept of breakdown defined in terms of definability and not in terms of bias. If a group of finite order k acts on the sample space we show that the breakdown point can be bounded above by (k−1)/k. In the case of directional data there is a group of order k=2 giving an upper bound of 1/2.

Citation

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P. Laurie Davies. Ursula Gather. "Addendum to the discussion of “Breakdown and groups”." Ann. Statist. 34 (3) 1577 - 1579, June 2006. https://doi.org/10.1214/009053606000000399

Information

Published: June 2006
First available in Project Euclid: 10 July 2006

zbMATH: 1113.62063
MathSciNet: MR2278369
Digital Object Identifier: 10.1214/009053606000000399

Subjects:
Primary: 62G35
Secondary: 62H11

Keywords: Breakdown , directional data , Equivariance

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 3 • June 2006
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