Let {[xi]j(t), t [set membership, variant] [0, T]} J = 1, 2 be infinitely divisible processes with distinct Poisson components and no Gaussian components. Let X be the set of all real-valued functions on [0, T] which are not identically zero, and be the [sigma]-ring generated by the cylinder...

A new synthetic representation of Student's t statistic is given which exhibits the random variable as a nonlinear function of two independent t variables. A generalization is given to the matricvariate t with an interpretation in terms of "natural conjugate" inference for multivariate normal...

Let (X1, X2,..., Xk, Y1, Y2,..., Yk) be multivariate normal and define a matrix C by Cij = cov(Xi, Yj). If (i) (X1,..., Xk) = (Y1,..., Yk) and (ii) C is symmetric positive definite, then 0 < varf(X1,..., Xk) < [infinity] => corr(f(X1,..., Xk),f(Y1,..., Yk)) 0. Condition (i) is necessary for the conclusion. The sufficiency of...</varf(x1,...,>

This paper presents a convergence theorem for an iterative method of spectral factorization in the context of multivariate prediction theory. It may be viewed as a constructive proof that the factorization exists, using only the analytic results of Hardy space theory.

The Robbins-Monro procedure for recursive estimation of a zero point of a regression function f is investigated for the case f defined on and with values in the space D[0, 1] of real-valued functions on [0, 1] that are right-continuous and have left-hand limits, endowed with Skorohod's...

The paper deals with the invariance principle for sums of independent identically distributed random variables. First it compares the different possibilities of posing the problem. The sharpest results of this theory are presented with a sketch of their proofs. At the end of the paper some...

In a paper by Lai [(1976) Ann. Statist. 4] a construction of sequences of confidence intervals for one-parameter exponential families is given, where the intersection of these intervals contains the true parameter value [theta]0 with a prescribed level of confidence and the respective interval...

We consider the notion of a spherically invariant measure on a real and separable Hilbert space and study some equivalence properties of measures of this type. The latter are of interest in statistical communication theory.