Robustness Measures: Bias and Breakdown Points

Abstract

In Chapter 3 robustness properties are derived by regarding the behaviour of estimators and corresponding functionals in infinitesimal neighbourhoods of the ideal distribution P_θδ. NOW, in Section 4.1 we will derive robustness properties of estimators by regarding the behaviour of their corresponding functionals in neighbourhoods which are not infinitesimal small. This behaviour is important for situations in which the amount of outliers is not decreasing to zero when the sample size is increasing to ∞. Moreover this robustness concept provides robustness measures, namely the bias and the breakdown point, which can be transferred to finite samples as is done in Section 4.2. In Section 4.3 the breakdown point for finite samples is derived for trimmed weighted L_pestimators in linear models, and in Section 4.4 it is investigated for nonlinear problems.