A local limit theorem for large deviations of o(n)1/2, where n is the sample size, is developed for multivariate statistics which are more general than standardised means, but which depend on n in much the same way. In particular, the cumulants of the statistic are of the same order in n-1/2 as...

The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form [integral operator]01 W dW, where W(r) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA...

A new series representation of the exact distribution of Hotelling's generalized T02 statistic is obtained. Unlike earlier work, the series representation given here is everywhere convergent. Explicit formulae are given for both the null and the non-central distributions. Earlier results by [1],...

It is shown that matrix quotients of submatrices of a spherical matrix are distributed as matrix Cauchy. This generalizes known results for scalar ratios of independent normal variates. The derivations are simple and make use of the theory of invariant measures on manifolds.

This paper studies the statistical properties of vector autoregressions (VAR's) for quite general multiple time series which are integrated processes of order one. Functional central limit theorems are given for multivariate partial sums of weakly dependent innovations and these are applied to...