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.

In estimation of the normal covariance matrix, finding a least favorable sequence of prior distributions has been an open question for a long time. This paper addresses the classical problem and accomplishes the specification of such a sequence, which establishes minimaxity of the best...

In this article, we consider the problem of testing the equality of mean vectors of dimension p of several groups with a common unknown non-singular covariance matrix Σ, based on N independent observation vectors where N may be less than the dimension p. This problem, known in the literature as...

This paper is concerned with estimation of a predictive density with parametric constraints under Kullback–Leibler loss. When an invariance structure is embedded in the problem, general and unified conditions for the minimaxity of the best equivariant predictive density estimator are derived....

The empirical best linear unbiased predictor (EBLUP) in the linear mixed model (LMM) is useful for the small area estimation, and the estimation of the mean squared error (MSE) of EBLUP is important as a measure of uncertainty of EBLUP. To obtain a second-order unbiased estimator of the MSE, the...

type="main" xml:id="sjos12040-abs-0001" <title type="main">ABSTRACT</title>Empirical Bayes (EB) estimates in general linear mixed models are useful for the small area estimation in the sense of increasing precision of estimation of small area means. However, one potential difficulty of EB is that the overall estimate for...

This paper treats the problem of estimating the restricted means of normal distributions with a known variance, where the means are restricted to a polyhedral convex cone which includes various restrictions such as positive orthant, simple order, tree order and umbrella order restrictions. In...

For the mean vector of a p-variate normal distribution (p [greater, double equals] 3), the generalized Bayes estimators dominating the James-Stein estimator under quadratic loss are given based on the methods of Brown, Brewster and Zidek for estimating a normal variance.