Bounds for the Bias of Estimators Under Contamination

The field of Robust Statistics deals with the problem of stability of estimators under a certain type of misspecification of the model with respect to the “true” and unknown distribution of the data. The word “stability” could be associated to the stability of the variance and/or of the bias of the estimators. Here, we provide lower bounds for the uniform maxbias function of an estimator under contamination. For some estimators we provide also an upper bound. We review results presented in the literature in a unified framework. We provide an example of the use of the results for the gamma parametric family.