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 their key remark in Section 6: " We know of no situation not based on equivariance considerations where it can be shown that the highest breakdown point for a class of reasonable functionals is less than 1. " Though we agree with their general point that one has to take care not to come up with void definitions, or put differently, to make the small print explicit, we want to draw attention to the relation of their results to an alternative definition of breakdown. In particular, we claim that a different perspective on the notion of breakdown may resolve some of the small print issues. The definition used by Davies and Gather in their equation (2.4) is a standard one and has its roots in the domain of location and scale estimation. As we argued in Genton and Lucas (2003), it is less useful in a setting with dependent data. For example, in a simple autoregression (AR) of order 1,