A decision theoretic structure for robust Bayesian analysis with applications to the estimation of a multivariate normal mean. (English) Zbl 0671.62011
Bayesian statistics 2, Proc. 2nd Int. Meet., Valencia/Spain 1983, 619-628 (1985).
Summary: [For the entire collection see Zbl 0659.00012.]
A robust Bayesian viewpoint that subjective prior information can only be quantified in terms of a class \(\Gamma\) of priors is assumed. It is then argued that it may be necessary to consider frequency criteria in choosing a decision rule corresponding to \(\Gamma\). An example concerning the estimation of a multivariate normal mean is considered. It is shown that under sum of squared errors loss, an estimator composed of several (more than one) independent Stein estimators can be improved upon in Bayes risk for suitably chosen classes of conjugate priors.
A robust Bayesian viewpoint that subjective prior information can only be quantified in terms of a class \(\Gamma\) of priors is assumed. It is then argued that it may be necessary to consider frequency criteria in choosing a decision rule corresponding to \(\Gamma\). An example concerning the estimation of a multivariate normal mean is considered. It is shown that under sum of squared errors loss, an estimator composed of several (more than one) independent Stein estimators can be improved upon in Bayes risk for suitably chosen classes of conjugate priors.
MSC:
| 62C10 | Bayesian problems; characterization of Bayes procedures |
| 62H12 | Estimation in multivariate analysis |
