The Annals of Statistics

Addendum to the discussion of “Breakdown and groups”

P. Laurie Davies and Ursula Gather

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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.

Article information

Source
Ann. Statist., Volume 34, Number 3 (2006), 1577-1579.

Dates
First available in Project Euclid: 10 July 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1152540760

Digital Object Identifier
doi:10.1214/009053606000000399

Mathematical Reviews number (MathSciNet)
MR2278369

Zentralblatt MATH identifier
1113.62063

Subjects
Primary: 62G35: Robustness
Secondary: 62H11: Directional data; spatial statistics

Keywords
Breakdown equivariance directional data

Citation

Davies, P. Laurie; Gather, Ursula. Addendum to the discussion of “Breakdown and groups”. Ann. Statist. 34 (2006), no. 3, 1577--1579. doi:10.1214/009053606000000399. https://projecteuclid.org/euclid.aos/1152540760


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