Breakdown and groups (vol 33, pg 977, 2005)
成果类型：
Correction
署名作者：
Davies, P. Laurie; Gather, Ursula
署名单位：
University of Duisburg Essen; Dortmund University of Technology
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/009053606000000399
发表日期：
2006
页码：
1577-1579
关键词：
摘要：
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.