منابع مشابه
Discussion of “ Breakdown and Groups ”
1. Introduction. In their interesting paper Davies and Gather draw our attention to what they call the " small print " in definitions of breakdown. Working from a formal group structure and a notion of equivariance, they show by a number of examples that a definition of breakdown may be void if not accompanied by a reasonable and precise group structure. This leads them to what we would label t...
متن کاملRejoinder to “ Breakdown and Groups
We thank all the discussants for their contributions and in particular we wish to thank Hampel. The concept of breakdown point goes back to his Ph.D. thesis [Hampel (1968)] and he was the first to exhibit a high breakdown equivariant regression estimate now known as the least median of squares [Hampel (1975)], a fact which is sometimes forgotten. These two sources are the starting point of the ...
متن کاملDiscussion of “ Breakdown and Groups ”
1. General comments. The interesting paper of Davies and Gather (henceforth [DG]) pulls together results on upper bounds on the breakdown value of translation equivariant location estimators [Donoho (1982)], regression esti-mators [Rousseeuw (1984)] and affine equivariant scatter estimators [Davies (1987)] into a single framework of group equivariance. I can only agree with them on the importan...
متن کاملDiscussion of “ Breakdown and Groups ”
1. Breakdown, equivariance and invariance. The authors are to be congratulated for their excellent paper, which nicely clarifies the role of equivariance in finding upper bounds for the breakdown points of functionals. The breakdown point approach, with upper bounds showing how far one can go, has achieved great success in the univariate and multivariate location, scale, scatter and regression ...
متن کاملDiscussion of “ Breakdown and Groups ”
The breakdown point has played an important role within robust statistics over the past 25–30 years. A large part of its appeal is that it is easy to explain and easy to understand. It is often interpreted as “the proportion of bad data a statistic can tolerate before becoming arbitrary or meaningless.” In this paper Professors Davies and Gather give us a much needed critical look at this seemi...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2005
ISSN: 0090-5364
DOI: 10.1214/009053604000001138