It is shown that the finite linear least-squares predictor of a multivariate stationary process converges to its Kolmogorov-Wiener predictor at an exponential rate, provided that the entries of its spectral density matrix are smooth functions. Also, the same rate of convergence holds for the...

This is a systematic and unified treatment of a variety of seemingly different strong limit problems. The main emphasis is laid on the study of the a.s. behavior of the rectangular means [zeta]mn = 1/([lambda]1(m) [lambda]2(n)) [Sigma]i=1m [Sigma]k=1n Xik as either max{m, n} -- [infinity] or...

Let {vij}, i, J = 1,2, ..., be i.i.d. random variables, and for each n let Mn = (1/s)VnVnT, where Vn = (vij), i = 1, 2, ..., n, j = 1, 2, ..., s = s(n), and n/s -- y 0 as n -- [infinity]. Necessary and sufficient conditions are given to establish the convergence in distribution of certain...

We consider the elliptical distribution of n p-dimensional random vectors X1, ..., Xn having p.d.f. of the form k(n, p) [Lambda]-n/2 g([Sigma]j=1n(Xj-[theta])' [Lambda]-1(Xj-[theta])) as a generalization of the multivariate normal distribution. Let A denote the Wishart matrix defined by , where...

A central limit theorem is obtained for orthogonally invariant random variables on n, the space of n - n real, positive definite symmetric matrices. The derivation requires the Taylor expansion of the spherical functions for the general linear group GL(n, R). This extends from the case n = 3 a...

We propose a stochastic differential equation approach to principal component analysis. We give the equations governing the spectrum of the square BTB of a n-p matrix of independent Brownian motions. We apply this result to P.C.A. of perturbed continuous data.

We give an elementary, direct proof that if an array of random variables {(Xij, [alpha], [xi]i, [eta]j); i, j [set membership, variant] } is separately exchangeable, then X = {Xij; i, j [set membership, variant] } and {([alpha], [xi]i, [eta]j); i, j [set membership, variant] } are conditionially...

Using the saddlepoint method, two explicit approximation formulae are given for the tail probability of Wilks' likelihood ratio criterion. A comparison with the exact probability shows that these approximations are very good even for small error degrees of freedom. A comparison with the...

This paper extends reduced-rank regression models for application to interaction in unequally replicated two-way classifications having no empty cells. The a - b matrix of interaction parameters is modeled as a linear function of a rank-[varrho] matrix, where [varrho] <= min[(a - 1), (b - 1)]. For fixed [varrho], the maximum likelihood estimator of the interaction matrix is derived. The likelihood ratio test of [varrho] = m versus [varrho] = m + r and a union-intersection test of [varrho] = 0 versus [varrho] >= r are constructed and...</=>