Clinical discussion groups

Minutes of Discussion Groups

Minutes of Discussion Groups

Discussion 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...

Discussion 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 ...

Discussion 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...