An analogue of the law of the iterated logarithm for Brownian motion in Banach spaces is proved where the expression [radical sign]2 loglog s is replaced by a positive non-decreasing function satisfying certain conditions.

Using a two stage regression procedure estimates of the unknown parameters of a class of multivariate random coefficient autoregressive models are obtained. The estimates are shown, under fairly general conditions, to be strongly consistent and to have a distribution which converges to that of a...

The first section of the paper introduces known theory relating to the description of the set of all ARMA structures via the concept of order, n, and the coordinatisation of all structures, M(n), of given order. The coordinates most easily used are related to the state space representation and...

Let V = (vij) denote the k - k symmetric scatter matrix following the Wishart distribution W(k, n, [Sigma]). The problem posed is to characterize the eigenfunctions of the expectation operators of the Wishart distribution, i.e., those scalar-valued functions f(V) such that (Enf)(V) =...

We prove the global Markov property for lattice systems of classical statistical mechanics, with bounded spins and finite range interactions. The method uses the one developed by two of us to prove the global Markov property of Euclidean generalized random fields. The result shows that the...

This paper derives conditions for the stationarity of a class of multiple autoregressive models with random coefficients. The models considered include as special cases those previously discussed by Andel (Ann. Math. Statist.42 (1971), 755-759; Math. Operationsforsch. Statist.7 (1976), 735-741).

In previous papers [Approximate and local Bahadur efficiency of linear rank tests in the two-sample problem, Ann. Statist.7, 1246-1255, 1979; Local comparison of linear rank tests in the Bahadur sense, Metrika, 1979] the author developed for linear rank tests of the one-sample symmetry and the...

For many testing problems several different tests may have optimal exact Bahadur slope. The introduction of Bahadur deficiency provides further information about the performance of such tests. Roughly speaking a sequence of tests is deficient in the sense of Bahadur of order (hn) at a fixed...

A recent theorem of T. L. Hai, H. Robbins, and C. Z. Wei (J. Multivariate Anal. 9 (1979), 343-362) is extended to a more general form which unifies previous results in the literature on the strong consistency of least squares estimates in multiple regression models with nonrandom regressors. In...