Hoeffding (Ann. Math. Statist. 1948) and Blum, Kiefer and Rosenblatt (Ann. Math. Statist. 1961) constructed distribution free tests of independence based on a multivariate empirical process. We establish strong invariance principles for the latter and also for appropriate functionals of it.

We show that an operator is absolutely summing if and only if it maps amarts into uniform amarts, from which we can deduce a theorem of A. Bellow and another of Edgar-Sucheston. We also show that the absolute value of a Banach lattice valued potential is a potential if and only if the lattice is...

Let ank, n >= 1, k >= 1, be a double array of real numbers and let Vn, n >= 1, be a sequence of random elements taking values in a separable Banach space. In this paper, we examine under what conditions the sequence [Sigma]k>=1ankVk, n >= 1, has a limit either in probability or almost surely.

In this paper we carry on our study [4] of the algebraic representations of general stochastic processes. We give methods for constructing the algebraic representation of a stochastic process from the distribution of the process at a fixed finite number of times, we develope some techniques of...

Previous work on the problem of estimating a univariate normal mean under squared error loss suggests that an estimator should be admissible if and only if it is generalized Bayes for a prior measure, F, whose tail is "light" in the sense that [integral operator]1[infinity] f*-1(x) DX =...

Optimization problems are connected with maximization of three functions, namely, geometric mean, arithmetic mean and harmonic mean of the eigenvalues of (X'[Sigma]X)-1[Sigma]Y(Y'[Sigma]Y)-1Y'[Sigma]X, where [Sigma] is positive definite, X and Y are p - r and p - s matrices of ranks r and s...

Conditions for mixed autoregressive-moving average processes with time-dependent coefficients to be purely nondeterministic and invertible can be obtained from classical difference equations theory. These conditions involve one-sided Green's functions or their matricial equivalents. A recursive...

Let (D) be the Schwartz space of infinitely differentiable scalar functions on the line, with compact supports, and ([Omega], [Sigma], P) be a fixed probability space. Let X : (D) -- L2([Omega], [Sigma], P) be a purely nondeterministic generalized random process (g.r.p.) in the sense of Itô...

A multivariate t vector X is represented in two different forms, one associated with a normal vector and an independent chi-squared variable, and the other with a normal vector and an independent Wishart matrix. We show that X is multivariate t with mean [mu], covariance matrix [nu]([nu] -...

In the present paper there is proposed a rank statistic for multivariate testing of randomness conceriing some marginal distributions. The asymptotic distribution of this statistic under hypothesis and "near" alternatives is treated.