Robustification Process on Bayes Estimators

The paper describes one possible robustification process on Bayes estimators and studies how a robust estimator can work with prior information. This robustification procedure, as one of possible sensitivity analysis, enables us to study the effect of the outlying observations together with sensitivity to a chosen prior distribution or to a chosen loss function. Consider i.i.d. d-dimensional random vectors X1, ...,Xn with a distribution Pθ depending on an unknown parameter θ in Θ R^l. We deal with robust counterparts of maximum posterior likelihood estimators and Bayes estimators in the inference on θ. Asymptotic properties of these robust versions, including their asymptotic equivalence of order op(n^−1), are proven.