ABSTRACT
A fundamental concept in robustness to outliers is the influence function (or curve), introduced by Hampel. “The importance of the influence function lies in its heuristic interpretation: it describes the effect of an infinitesimal contamination at the point x on the estimate, standardized by the mass of the contamination”. In general, maximum likelihood estimation leads to parameter estimators with unbounded influence functions for some or all parameters. Hence maximum likelihood estimators are generally vulnerable to the unbounded influence of even a single outlier. Outlier values may be gross errors due to ’contamination’, in which case they need to be identified and removed. A robust fitted model is a good way to identify gross errors. Alternatively outlier values may be genuine values, in which case the model may be wrong, since extreme outliers are unlikely to occur.
