Comprehensive Definitions of Breakdown-Points for Independent and Dependent Observations

We provide a new definition of breakdown in finite samples with an extension to asymptotic breakdown. Previous definitions center around defining 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 contract to the traditional approach, we leave the definition of the critical region implicit. Our definition encompasses all previous definitions of breakdown in both linear and non-linear regression settings. In some cases, it leads to a different notion of breakdown than other procedures available. An advantage is that our new definition also applied to models for dependent observations (time-series, spatial statistics) where currenty breakdown definitions typically fail. We illustrate our points using examples from linear and non-linear regression as well as time-series and spatial statistics.