Addendum to the discussion of "Breakdown and Groups"

P.L. Davies, U. Gather

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Samenvatting

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.
Originele taal-2Engels
Pagina's (van-tot)1577-1579
TijdschriftThe Annals of Statistics
Volume34
Nummer van het tijdschrift3
DOI's
StatusGepubliceerd - 2006

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