The exact distribution of Mauchly's sphericity test criterion W = S/[trS/p]p, when S is the sum of product matrix from a sample of size N taken from a p-variate normal population, is obtained using contour integration and methods similar to those of Nair and Box. Tables of percentage points for...

Let G be a discrete locally compact abelian group. Let (xg)g[set membership, variant]G be a q-variate weakly stationary stochastic process indexed by elements g of G. A. N. Kolmogorov, P. Masani, H. Salehi and others have derived numerous results on the minimality and interpolation of random...

We extend the invariance principle to triangular arrays of Banach space valued random variables, and as an application derive the invariance principle for lattices of random variables. We also point out how the q-dimensional time parameter Yeh-Wiener process is naturally related to a one...

The asymptotic expansions are derived up to terms of order 1/n, for the c.d.f. and percentile of the statistic T = m Tr S1S2-1, where mS1 and nS2 are independently distributed W(m, p, [Sigma]1) and W(n, p, [Sigma]2), respectively. The expansions hold when [Sigma]1[Sigma]2-1 = I + E and Chi(E) ...

In [6, theorem IV.8.18], relatively norm compact sets K in Lp([mu]) are characterized by means of strong convergence of conditional expectations, E[pi]f -- f in Lp([mu]), uniformly for f [set membership, variant] K, where (E[pi]) is the family of conditional expectations corresponding to the net...

The paper deals with statistical inference for a certain class of bivariate distributions. The class of marginal distributions is given and is shown to include distributions with only location and scale parameters. A normalizing transformation is applied to the marginal distributions and the...

In this paper, the authors consider the evaluation of the distribution functions of the ratios of the intermediate roots to the trace of the real Wishart matrix as well as the ratios of the individual roots to the trace of the complex Wishart matrix. In addition, the authors consider the...

Some key theorems in the asymptotic theory for multivariate time series, using spectrl methods, are established. These theorems relate to various estimation situations including multiple systems of regressions, the determination of the frequency of a periodic signal and the determination of the...

For testing the hypothesis of equality of two covariances ([Sigma]1 and [Sigma]2) of two p-dimensional multivariate normal populations, it is shown that the power function of the modified likelihood ratio test increases as [lambda]1 increases from one and [lambda]r decreases from one where...

Closed form matrix equations are given for the information matrix of the parameters of the vector mixed autoregressive moving average time series model.