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...

This paper is concerned with the problem of estimating a matrix of means in multivariate normal distributions with an unknown covariance matrix under invariant quadratic loss. It is first shown that the modified Efron-Morris estimator is characterized as a certain empirical Bayes estimator. This...

This paper treats the problem of estimating positive parameters restricted to a polyhedral convex cone which includes typical order restrictions, such as simple order, tree order and umbrella order restrictions. In this paper, two methods are used to show the improvement of order-preserving...

This paper deals with the problem of estimating the normal covariance matrix relative to the Stein loss. The main interest concerns a new class of estimators which are invariant under a commutator subgroup of lower triangular matrices. The minimaxity of a James–Stein type invariant estimator...

This paper deals with the problem of estimating the mean matrix in an elliptically contoured distribution with unknown scale matrix. The Laplace and inverse Laplace transforms of the density allow us not only to evaluate the risk function with respect to a quadratic loss but also to simplify...

This paper addresses the problem of estimating the normal mean matrix in the case of unknown covariance matrix. This problem is solved by considering generalized Bayesian hierarchical models. The resulting generalized Bayes estimators with respect to an invariant quadratic loss function are...

The problem of estimating the precision matrix of a multivariate normal distribution model is considered with respect to a quadratic loss function. A number of covariance estimators originally intended for a variety of loss functions are adapted so as to obtain alternative estimators of the...

In some invariant estimation problems under a group, the Bayes estimator against an invariant prior has equivariance as well. This is useful notably for evaluating the frequentist risk of the Bayes estimator. This paper addresses the problem of estimating a matrix of means in normal...

In linear mixed models, the conditional Akaike Information Criterion (cAIC) is a procedure for variable selection in light of the prediction of specific clusters or random effects. This is useful in problems involving prediction of random effects such as small area estimation, and much attention...

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...