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 centre on defining a critical region for either the parameter or the objective function. If for a particular outlier configuration the critical region is entered, breakdown is said to occur. In contrast with the traditional approach, we leave the definition of the critical region implicit. Our proposal encompasses previous definitions of breakdown in linear and non-linear regression settings. In some cases, it leads to a different and more intuitive notion of breakdown than other procedures that are available. An important advantage of our new definition is that it also applies to models for dependent observations where current definitions of breakdown typically fail. We illustrate our suggestion by using examples from linear and non-linear regression, and time series.