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 -...

Zellner ((1994) in: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics. Springer, New York, pp. 371-390), introduced the notion of a balanced loss function in the context of a general linear model to reflect both goodness of fit and precision of estimation. We study...

Bayes estimation of the mean of a variance mixture of multivariate normal distributions is considered under sum of squared errors loss. We find broad class of priors (also in the variance mixture of normal class) which result in proper and generalized Bayes minimax estimators. This paper extends...

Consider the problem of estimating the mean vector [theta] of a random variable X in , with a spherically symmetric density f(||x-[theta]||2), under loss ||[delta]-[theta]||2. We give an increasing sequence of bounds on the shrinkage constant of Stein-type estimators depending on properties of...

We consider estimation of a location vector in the presence of known or unknown scale parameter in three dimensions. The technique of proof is Stein's integration by parts and it is used to cover several cases (e.g., non-unimodal distributions) for which previous results were known only in the...

In the GMANOVA model or equivalent growth curve model, shrinkage effects on the MLE (maximum likelihood estimator) are considered under an invariant risk matrix. We first study the fundamental structure of the problem through which we decompose the estimation problem into some conditional...

Families of minimax estimators are found for the location parameters of a p-variate distribution of the form , where G(·) is a known c.d.f. on (0, [infinity]), p = 3 and the loss is sum of squared errors. The estimators are of the form (1 - ar(X'X)/E0(1/X'X)X'X)X where 0 = a = 2, r(X'X) is...

Let X~f([short parallel]x-[theta][short parallel]2) and let [delta][pi](X) be the generalized Bayes estimator of [theta] with respect to a spherically symmetric prior, [pi]([short parallel][theta][short parallel]2), for loss [short parallel][delta]-[theta][short parallel]2. We show that if...

This paper extensively investigates the theory of estimating the regression coefficient matrix for the normal GNANOVA model. We explicitly construct estimators which improve the maximum likehood estimator under an invariant scalar loss function. These include the double shrinkage estimators and...