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....

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 consider stochastic domination in predictive density estimation problems when the underlying loss metric is α-divergence, D(α), loss introduced by Csiszàr (1967). The underlying distributions considered are normal location-scale models, including the distribution of the observables, the...

We investigate conditions under which estimators of the form X + aU'Ug(X) dominate X when X, a p - 1 vector, and U, an m - 1 vector, are distributed such that [X1, X2,..., Xp, U1, U2,..., Up]'/[sigma] has a spherically symmetric distribution about [[theta]1, [theta]2,..., [theta]p, 0, 0,...,...

We consider the problem of estimating a p-dimensional parameter [theta]=([theta]1,...,[theta]p) when the observation is a p+k vector (X,U) where dim X=p and where U is a residual vector with dim U=k. The distributional assumption is that (X,U) has a spherically symmetric distribution around...

Assume X = (X1, ..., Xp)' is a normal mixture distribution with density w.r.t. Lebesgue measure, , where [Sigma] is a known positive definite matrix and F is any known c.d.f. on (0, [infinity]). Estimation of the mean vector under an arbitrary known quadratic loss function Q([theta], a) = (a -...

When estimating, under quadratic loss, the location parameter[theta]of a spherically symmetric distribution with known scale parameter, we show that it may be that the common practice of utilizing the residual vector as an estimate of the variance is preferable to using the known value of the...

We derive minimax generalized Bayes estimators of regression coefficients in the general linear model with spherically symmetric errors under invariant quadratic loss for the case of unknown scale. The class of estimators generalizes the class considered in Maruyama and Strawderman [Y. Maruyama,...

Let X,V1,...,Vn-1 be n random vectors in with joint density of the formwhere both [theta] and [Sigma] are unknown. We consider the problem of the estimation of [theta] with the invariant loss ([delta]-[theta])'[Sigma]-1([delta]-[theta]) and propose estimators which dominate the usual estimator...