Robustification Process on Bayes Estimators

Abstract

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 $X_1,...,X_n$ with a distribution $P_\theta $ depending on an unknown parameter $\underset{\sim}{\theta} \in \Theta \subset R^l.$ We deal with robust counterparts of maximum posterior likelihood estimators and Bayes estimators in the inference on $\theta.$ Asymptotic properties of these robust versions, including their asymptotic equivalence of order $o_p (n^{ - 1} ),$ are proven. Keywords: Bayes type estimators; robustification process; asymptotic theory. Closure matroid.