The moving average representations of discrete multidimensional stationary processes are generalized to fundamental moving average representations of weakly harmonizable processes. For strongly harmonizable processes, necessary and sufficient conditions on covariance functions are obtained for...

We obtain approximations to the distribution of the exponent in the matrix Fisher distributions on SO(p) and on O(p) whose density with respect to Haar measure is proportional to exp(Tr GX0tX). Similar approximations are found for the distribution of the exponent in the Bingham distribution,...

Let X1, X2, ..., Xn be random vectors that take values in a compact set in Rd, d = 1. Let Y1, Y2, ..., Yn be random variables ("the responses") which conditionally on X1 = x1, ..., Xn = xn are independent with densities f(y xi, [theta](xi)), i = 1, ..., n. Assuming that [theta] lives in a...

Let E' be the separable dual of a Banach space E, and the class of all nonempty, convex, weak*-compact subsets od E'. J. Neveu proved the convergence of -valued martingales called multivalued martingales. We prove Riesz approximations for some multivalued processes; i.e., for these processes, we...

A set of n points sampled from a common distribution F, is partitioned into k = 2 groups that maximize the between group sum of squares. The asymptotic normality of the vector of probabilities of lying in each group and the vector of group means is known under the condition that a particular...

For testing that a distribution is invariant under the action of a finite group (e.g., the distribution is exchangeable) a most powerful test, against a specific alternative, among the class of tests invariant under a second, arbitrary group is obtained. After a class of permutation tests...

The asymptotic distribution of some test criteria for a covariance matrix are derived under local alternatives. Except for the existence of some higher moments, no assumption as to the form of the distribution function is made. As an illustration, a case of t distribution included normal model...

For orthogonally invariant estimation of [Sigma] of Wishart distribution using Stein's loss, any estimator which does not preserve the order of the sample eigenvalues is dominated by a modified estimator preserving the order.

Two optimal characteristic properties of the normal distribution are shown: (a) Of all the SNM (spherical scale normal mixtures) the normal with the same Mahalanobis distances between [Pi]i:SNM([mu]i) and [Pi]j:SNM([mu]j), i [not equal to] j, maximizes the probabilities of correct classification...

In multivariate discrimination of two normal populations, the optimal classification procedure is based on the quadratic discriminant function. We investigate asymptotic properties of this function if the covariance matrices of the two populations are estimated under the following four models;...