In the multivariate case, the empirical dependence function, defined as the empirical distribution function with reduced uniform margins on the unit interval, can be shown for an i.i.d. sequence to converge weakly in an asymptotic way to a limiting Gaussian process. The main result of this paper...

Kantorovich gave an upper bound to the product of two quadratic forms, (X'AX) (X'A-1X), where X is an n-vector of unit length and A is a positive definite matrix. Bloomfield, Watson and Knott found the bound for the product of determinants X'AX X'A-1X where X is n - k matrix such that X'X = Ik....

Motivated by problems occurring in the empirical identification and modelling of a n-dimensional ARMA time series X(t) we study the possibility of obtaining a factorization (I + a1B + ... + apBp) X(t) = [[Pi]i=1p (I - [alpha]iB)] X(t), where B is the backward shift operator. Using a result in...

The theory of elliptically contoured distributions is presented in an unrestricted setting, with no moment restrictions or assumptions of absolute continuity. These distributions are defined parametrically through their characteristic functions and then studied primarily through the use of...

The tetrachoric series is a technique for evaluating multivariate normal probabilities frequently cited in the statistical literature. In this paper we have examined the convergence properties of the tetrachoric series and have established the following. For orthant probabilities, the...

Stochastic integration of left continuous integrands with respect to quasimartingales is developed as the pathwise limit of Riemann-Stieltjes sums. The procedure is extended to right continuous integrands.

A tolerance region is a map from the sample space of one statistical model to the event space of a second statistical model having the same parameter. This paper derives an optimum [beta]-expectation tolerance region for the multivariate regression model. A measure of power is proposed and...

. Let E and F be Banach spaces, and U: E -- F a bounded linear operator. The following are equivalent: 1. o2. (a) U is an Asplund operator.3. (b) Let (Xn) be a sequence of Bochner measurable functions with values in E and supn||;Xn|| [infinity] a.e. If (Xn) converges scalarly to 0 in E, then...

For any class Q of distributions on Rd, let (Q) be the class of limit distributions of bn-1(X1 + ... + Xn) - an, where {Xn} are independent Rd-valued random variables, each with distribution in Q, bn 0, an [set membership, variant] Rd, and {bn-1Xj} is a null array. When Q is the class of all...