Generalized Bayesian-type estimators. Robust and sensitivity analysis
Jan Hanousek · Czech digital mathematics library · 1994
JAN HANOUSEKLet Xi, X2,... ,X n , be i.i.d.random variables with a density function f(x,9) where 0 £ 0 C R k is an unknown parameter that we are interested in estimating.Following up robustification procedure presented by Huber [10] we shall study one possible approach for using (non-sample) prior information for robust type estimators and prove some asymptotic properties of introduced estimators.We shall show that the Bayes-type estimators and maximum posterior probability estimators are asymptotically equivalent to the order Op(» -1 ) or o p (n -1 ), depending on some regularity conditions.Because of this asymptotic relation, one expects that with an appropriate choice of p (i. e such as we would use in generating an M-estimator) we can obtain a Bayesian type estimator with good robustness properties.In addition, if f(x, 9) = exp{-p(X % , 0)} then these results lead to relations of maximum likelihood and Bayes' estimators.