For a finite measure d[Delta] on R1 the closed linear span in Lp(d[Delta]) of the exponentials {eiix: [short parallel] t [short parallel] = T} is discussed. These results are applied in the characterization of the spectral densities of stationary Gaussian processes which exhibit a Markovian...

A detailed study of the structure of conditional expectations and conditional probability measures is presented. Some characterizations of conditional expectations as a subclass of projection operators on Banach function spaces, and similarly conditional probabilities as a subclass of vector...

A vector definition of multivariate hazard rate, and associated definitions of increasing and decreasing multivariate hazard rate distributions are presented. Consequences of these definitions are worked out in a number of special cases. Relationships between hazard rate and orthant dependence...

Asymptotic expansions are given for the density function of the normalized latent roots of S1S2-1 for large n under the assumption of [Omega] = O(n), where S1 and S2 are independent noncentral and central Wishart matrices having the Wp(b, [Sigma]; [Omega]) and Wp(n, [Sigma]) distributions,...

The modified likelihood ratio criterion for testing the homogeneity of variances of p univariate normal populations, and the sphericity test, are both shown in this paper to have a monotone nondecreasing power function.

A theorem is proved that characterizes multivariate distribution functions of class L. This theorem is used to show that every n-dimensional, symmetric distribution function of class L is unimodal in the sense of Kanter.

Given a suitable function Fn we define a class of estimators called asymptotic Fn-estimators (i.e., estimators which approximate the solution of Fn([theta]) = 0). It is proved that this class is nonvoid if appropriate regularity conditions are fulfilled and if one has at hand a suitable initial...

A continuous-parameter ascending amart is a stochastic process (Xt)t[set membership, variant]+ such that E[X[tau]n] converges for every ascending sequence ([tau]n) of optional times taking finitely many values. A descending amart is a process (Xt)t[set membership, variant]+ such that E[X[tau]n]...

Let X be a p-variate (p = 3) vector normally distributed with mean [theta] and known covariance matrix . It is desired to estimate [theta] under the quadratic loss ([delta] - [theta])t Q([delta] - [theta]), where Q is a known positive definite matrix. A broad class of minimax estimators for...

This paper deals with maximum likelihood estimation of linear or nonlinear functional relationships assuming that replicated observations have been made on p variables at n points. The joint distribution of the pn errors is assumed to be multivariate normal. Existing results are extended in two...