In this paper the distribution of the likelihood ratio test for testing the reality of the covariance matrix of a complex multivariate normal distribution is investigated. Some simplifications in the noncentral distribution are made and the noncentral distribution is derived for the special case...

Let {W(t): t >= 0} be [mu]-Brownian motion in a real separable Banach space B, and let aT be a nondecreasing function of T for which (i) 0 < aT <= T (T >= 0), (ii) aT/T is nonincreasing. We establish a Strassen limit theorem for the net {[xi]T: T >= 3}, where

This paper is a continuation of the study made in [38]. Using Douglas' operator range theorem and Crimmins' corollary we obtain several new results on the "square-integrability of operator-valued functions with respect to a nonnegative hermitian measure". Using these facts we are able to extend...

The ordinary notion of a bivariate distribution has a natural generalisation. For this generalisation it is shown that a bivariate distribution can be characterised by a Hilbert space and a family p, 0 = p = 1, of subspaces of . specifies the marginal distributions whilst p is a summary of the...

A generalization of a vector-valued integral arising in the noncommutative (quantum) statistical decision theory is considered.

In this paper the author tries to give general conditions for the existence of Bayes estimates and for the consistency of sequences of Bayes estimates. In Section 3 we prove existence theorems for Bayes estimates, which contain those of [3], as a special case. The proof is based on a theorem of...

In this paper we establish three theorems concerning the asymptotic distributions of ordinary least-squares estimates of the parameters of a stochastic difference equation. We show that, if there is at least one root of the associated characteristic equation with modulus less than one and if all...

It is shown that the representation theory of a multivariate, purely nondeterministic, wide sense stationary generalized process can be reduced to a study of some isomorphism results established for commutation relations occurring in quantum mechanics. Using this simplification a multiplicity...

The problem of estimating the regression coefficient matrix having known (reduced) rank for the multivariate linear model when both sets of variates are jointly stochastic is discussed. We show that this problem is related to the problem of deciding how many principal components or pairs of...

For statistical decision problems, there are two well-known methods of randomization: on the one hand, randomization by means of mixtures of nonrandomized decision functions (randomized decision rules) in the game "statistician against nature," on the other hand, randomization by means of...