Robust model-based clustering with mild and gross outliers

We propose a model-based clustering procedure for mild and gross outliers. Our mixture model is based on heavy-tailed components (e.g., the contaminated normal distribution), but it is assumed to apply only to a subset of the data. Consequently, a proportion of observations is trimmed. We propose a penalized likelihood approach for estimation and selection of the proportions of mild and gross outliers, where the penalty parameter is fixed by formal optimality arguments. We conclude with an original real data example on the identification of the source from illicit drug shipments seized in Italy and Spain.