Robustness of ML estimators of location-scale mixtures

The robustness of ML estimators for mixture models with fixed and estimated number of components s is investigated by the definition and computation of a breakdown point for mixture model parameters and by considering some artificial examples. The ML estimator of the Normal mixture model is compared with the approach of adding a "noise component" (Fraley and Raftery (1998)) and by mixtures of t-distributions (Peel and McLachlan (2000)). It turns out that the estimation of the number of mixture components is crucial for breakdown robustness. To attain robustness for fixed s, the addition of an improper noise component is proposed. A guideline to choose a lower scale bound is given.