For X one observation on a p-dimensional (p = 4) spherically symmetric (s.s.) distribution about [theta], minimax estimators whose risks dominate the risk of X (the best invariant procedure) are found with respect to general quadratic loss, L([delta], [theta]) = ([delta] - [theta])' D([delta] -...

We shall consider the decomposition problem of multivariate infinitely divisible characteristic functions which have no Gaussian component and have absolutely continuous Poisson spectral measures. Under the condition that A = {x;f(x) 0} is open, where f is the density of spectral measure, we...

Preliminary test estimators are defined for estimating vector parameters. This note illustrates the use of the Rao-Blackwell theorem for uniformly reducing the risk of these estimators when one is based upon the sufficient statistic. The results given are valid for a class of risk functions,...

The object of the present investigation is to show that the elegant asymptotic almost-sure representation of a sample quantile for independent and identically distributed random variables, established by Bahadur [1] holds for a stationary sequence of [phi]-mixing random variables. Two different...

The main aim of this paper is to solve the functional equations and k 1, in vector variables t1,...,tk satisfying the condition ti = ([Sigma]j = 1m tij2)1/2 [delta] for all i, where C[alpha]i, B[alpha]j and Aij are given square matrices and d[alpha] is a given vector. The elements of the...

Let [theta](n) denote the maximum likelihood estimator of a vector parameter, based on an i.i.d. sample of size n. The class of estimators [theta](n) + n-1 q([theta](n)), with q running through a class of sufficiently smooth functions, is essentially complete in the following sense: For any...

The limit theorems for polylinear forms are obtained. Conditions are found under which the distribution of the polylinear form of many random variables is essentially the same as if all the distributions of arguments were normal.

In this paper, the authors propose a locally most powerful invariant test for the equality of means in the presence of covariate variables. Also the null and nonnull distributions associated with the above test are developed. This problem arises in covariate discriminant analysis and has been...

Let Sp-p ~ Wishart ([Sigma], k), [Sigma] unknown, k p + 1. Minimax estimators of [Sigma]-1 are given for L1, an Empirical Bayes loss function; and L2, a standard loss function (Ri [reverse not equivalent] E(Li | [Sigma]), I = 1, 2). The estimators are , a, b = 0, r(·) a functional on...