We consider minimax shrinkage estimation of location for spherically symmetric distributions under a concave function of the usual squared error loss. Scale mixtures of normal distributions and losses with completely monotone derivatives are featured.

This paper obtains conditions for minimaxity of hierarchical Bayes estimators in the estimation of a mean vector of a multivariate normal distribution. Hierarchical prior distributions with three types of second stage priors are treated. Conditions for admissibility and inadmissibility of the...

This paper studies minimaxity of estimators of a set of linear combinations of location parameters [mu]i, i=1,...,k under quadratic loss. When each location parameter is known to be positive, previous results about minimaxity or non-minimaxity are extended from the case of estimating a single...

We introduce a family of bivariate discrete distributions whose members are generated by a decreasing mass function <italic>p</italic>, and with margins given by <italic>p</italic>. Several properties and examples are obtained, including a family of seemingly novel bivariate Poisson distributions.

For estimating a bounded normal mean with known variance, we exhibit situations of pronounced discrepancy between the credibility of Bayes credible regions and frequentist coverage. Analogously, frequentist confidence intervals are shown to have credibility one in some cases.

For a vast array of general spherically symmetric location-scale models with a residual vector, we consider estimating the (univariate) location parameter when it is lower bounded. We provide conditions for estimators to dominate the benchmark minimax MRE estimator, and thus be minimax under...