Breakdowns and Groups 
Professor Ursula Gather, Department of Statistics,Universität Dortmund, Dortmund, Germany

Monday, Oct 18, 2004, 4:10 PM
319 Snedecor

The concept of breakdown point was introduced by Hampel (1968, 1971) and developed further by among others Huber (1981) and Huber and Donoho (1983). It has proved most successful in the context of location, scale and regression problems. Attempts to extend the concept to other situations have not met with general acceptance. In this seminar we argue that this is connected to the fact that in the location, scale and regression problems the translation and affine groups give rise to a definition of equivariance for statistical functionals. Comparisons in terms of breakdown points seem only useful when restricted to equivariant functionals and even here the connection between breakdown and equivarance is a tenuous one.