Asymptotic expansions of the joint distributions of the latent roots of the Wishart matrix and multivariate F matrix are obtained for large degrees of freedom when the population latent roots have arbitrary multiplicity. Asymptotic expansions of the distributions of the latent vectors of the...

The strong consistency of least squares estimates in multiple regression models is established under minimal assumptions on the design and weak dependence and moment restrictions on the errors.

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...

Bounds for several integrals (tail probabilities, for example) are established by showing that each integral is a Schur function.

Orthogonal polynomials on the multivariate negative binomial distribution, where [alpha] > 0, [Theta]1 > 0, X = [Sigma] [Theta]i, x0, x1, ..., xp = 0,1, ... are constructed and their properties studied.

Let P[eta], [eta] = ([theta], [gamma]) [set membership, variant] [Theta] - [Gamma] [subset of] - k, be a (k + 1)-dimensional exponential family. Let [phi]n*, n [set membership, variant] , be an optimal similar test for the hypothesis {P([theta],[gamma])n: [gamma] [set membership, variant]...

The asymptotic distribution of multivariate M-estimates is studied. It is shown that, in general, consistency leads to asymptotic normality and a Law of the Iterated Logarithm. The results are used to compute via matrix derivatives the asymptotic distribution of a class of estimates due to Maronna.

It is established that a vector (X'1, X'2, ..., X'k) has a multivariate normal distribution if (i) for each Xi the regression on the rest is linear, (ii) the conditional distribution of X1 about the regression does not depend on the rest of the variables, and (iii) the conditional distribution...

Using the method of algebraic models, it is proved first that the projective limit T of a projective system of measure preserving transformations T[alpha] exists and is unique, modulo conjugacy, and then that if T[alpha] are ergodic with discrete spectrum, or totally ergodic (all iterates...

It is shown that if X1, X2, ..., Xn are symmetric random variables and max(X1, ..., Xn)+ = max(0, X1, ..., Xn), then E[max(X1,...,Xn)+]=[max(X1,X1,+X2,+X1,+X3,...X1,+Xn)+], and in the case of independent identically distributed symmetric random variables, E[max(X1, X2)+] = E[(X1)+] + (1/2)E[(X1...