Optimal and minimax prediction in multivariate normal populations under a balanced loss function

Minimax estimation of multivariate normalmean under balanced loss function 1

This paper considers simultaneous estimation of multivariate normal mean vector using Zellner's(1994) balanced loss function when 2 is known and unknown. We show that the usual estimator X is minimax and obtain a class of minimax estimators which have uniformly smaller risk than the usual estimator X. Also, we obtain the proper Bayes estimator relative to balanced loss function and nd the minim...

Estimation of the Multivariate Normal Mean under the Extended Reflected Normal Loss Function

Simultaneous Estimation of the Multivariate Normal Mean under Balanced Loss Function

This paper considers simultaneous estimation of multivariate normal mean vector using Zellner's(1994) balanced loss function which is deened as follows :

Estimating a Bounded Normal Mean Under the LINEX Loss Function

Let X be a random variable from a normal distribution with unknown mean θ and known variance σ2. In many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. As the usual estimator of θ, i.e., X under the LINEX loss function is inadmissible, finding some competitors for X becomes worthwhile. The only study in the literature considered the problem of min...

Improved Minimax Prediction Under Kullback-Leibler Loss

Let X | μ ∼ Np(μ, vxI) and Y | μ ∼ Np(μ, vyI) be independent p-dimensional multivariate normal vectors with common unknown mean μ, and let p(x|μ) and p(y |μ) denote the conditional densities of X and Y . Based on only observing X = x, we consider the problem of obtaining a predictive distribution p̂(y |x) for Y that is close to p(y |μ) as measured by Kullback-Leibler loss. The natural straw man ...