Breakdown and Groups II - P. Laurie Davies; Ursula Gather (Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 2004)
The notion of breakdown point was introduced by Hampel (1968, 1971) and has since played an important role in the theory and practice of robust statistics. In Davies and Gather (2004) it was argued that the success of the concept is connected to the existence of a group of transformations on the sample space and the linking of breakdown and equivariance. For example the highest breakdown point of any translation equivariant functional on the real line is 1/2 whereas without equivariance considerations the highest breakdown point is the trivial upper bound of 1.
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