We extend and generalize to the multivariate set-up our earlier investigations related to expected remaining life functions and general hazard measures including representations and stability theorems for arbitrary probability distributions in terms of these concepts. (The univariate case is...

Let E be a locally convex space. Then E is nuclear metrizable if and only if there exists a [sigma]-additive measure [mu] on E' such that L: E -- L0(E', [mu]), L(x) = <x, ·>, is an isomorphism. Let E be quasi-complete or barrelled. Suppose that there exists a [sigma]-additive measure [nu] on E...</x,>

An analytic characterization of stationary fields with a positive angle between the vertical past and future, in the sense of Helson and Lowdenslager, is given. The connection between the positivity of the angle and the convergence of the Fourier series for certain functions is studied. The case...

We prove that every harmonizable process with [sigma]-finite bimeasure is asymptotically stationary and we give its associated spectral measure.

Suppose one has two measures of dependence between two or more families of random variables. One of the measures is said to "dominate" the other if the latter becomes arbitrarily small as the former becomes sufficiently small. A description is given of the entire pattern of dominations between...

Let (X, Y) be a pair of random variables such that X = (X1,..., Xd) ranges over a nondegenerate compact d-dimensional interval C and Y is real-valued. Let the conditional distribution of Y given X have mean [theta](X) and satisfy an appropriate moment condition. It is assumed that the...

An earlier paper by the author ([4], 97-114) established large deviation local limit theorems for arbitrary sequences of real valued random variables. This work showed clearly the connection between the Cramér series and large deviation rates. In this article we present large deviation local...

A random sample of continuous measurements can be partitioned into g groups or clusters by minimizing the within group dispersion as measured by the 1-norm. The central limit theory associated with such partitions which are universally optimal or locally optimal is derived. A procedure is...

A method is given for constructing a prediction region having smallest expected measure within the class of invariant level [beta] prediction regions. The main assumptions are that the invariance group acts transitively on the parameter space and that the measure satisfies a certain invariance...