Strassen's version of the law of the iterated logarithm is extended to the two-parameter Gaussian process {X(s, t); [epsilon](s, t) [set membership, variant][0, [infinity])2} with the covariance function R((s1,t1),(s2,t2)) = min(s1,s2)min(t1,t2).

The purpose of this paper is to show the equivalence of almost sure convergence of Sn/n, n = 1 and lim supn--[infinity]||Sn||/n [infinity] a.e., where Sn = X1 + X2 + ... + Xn and X1, X2,... are independent identically distributed random elements in a separable Banach space with E||X1|| ...

This paper presents a necessary and sufficient condition for the weak convergence of uniform measures on an arbitrary Hausdorff uniform space in terms of their projections in metric spaces. This result was inspired by and extends a result of Bartoszynski which characterizes the weak convergence...

A multivariate linear relation [eta]n = [beta]0[xi]n is considered, in which [xi]n and [eta]n are observed subject to white noise errors, with covariance matrices [sigma]0, [omega]0 respectively. If their elements lie in the null space of a suitable vector function, [beta]0, [sigma]0, [omega]0...

It is shown that for the MANOVA problem the power function of the test based on the trace of a multivariate beta matrix is monotonically increasing in each noncentrality parameter provided that the cutoff point is not too large. This result is also true for the problem of testing independence of...

In this paper, the authors obtained asymptotic expressions for the joint distributions of certain functions of the eigenvalues of the Wishart matrix, correlation matrix, MANOVA matrix and canonical correlation matrix when the population roots have multiplicity.

Let [Omega] be a finite set with k elements and for each integer n [greater, double equals] 1 let [Omega]n = [Omega] - [Omega] - ... - [Omega] (n-tuple) and 11 and aj [not equal to] aj+1 for some 1 [less, double equals] j [less, double equals] n - 1}. Let {Ym} be a sequence of independent and...

Laws of large numbers, central limit theorems, and laws of the iterated logarithm are obtained for discrete and continuous time Markov processes whose state space is a set of measures. These results apply to each measure-valued stochastic process itself and not simply to its real-valued functionals.

Let X(t) and Y(t) be two stochastically continuous processes with independent increments over [0, T] and Lévy spectral measures Mt and Nt, respectively, and let the "time-jump" measures M and N be defined over [0, T] - [-45 degree rule]{0} by M((t1, t2] - A) = Mt2(A) - Mt1(A) and N((T1, t2] -...

The nonnull distribution of some statistics, used for testing [Sigma]1 = [Sigma]2 are obtained as mixtures of incomplete beta functions as well as mixtures of incomplete gamma functions. The introduction of the convergence factors and certain recurrence relations are useful in the computation of...