Comprehensive Definitions of Breakdown-Points for Independent and Dependent Observations

We provide a new de nition of breakdown in nite samples with an extension to asymptotic breakdown. Previous de nitions center around de ning a critical region for either the parameter or the objective function. If for a particular outlier constellation the critical region is entered, breakdown is said to occur. In contrast to the traditional approach, we leave the de nition of the critical region implicit. Our de nition encompasses all previous de nitions of breakdown in both linear and non-linear regression settings. In some cases, it leads to a di erent notion of breakdown than other procedures available. An advantage is that our new de nition also applies to models for dependent observations (time-series, spatial statistics) where current breakdown de nitions typically fail. We illustrate our points using examples from linear and non-linear regression as well as time-series and spatial statistics.