Many authors have discussed maximum likelihood estimation in the simple linear functional relationship model. In this paper, we derive maximum likelihood estimators (MLEs) for parameters in a much more general model. Several special cases including the multivariate linear functional relationship...

A common problem in multivariate analysis is that of minimizing a scalar function [phi] of a positive semidefinite matrix A subject possibly to AX = 0. In this paper it is suggested to replace A by B'B, where B is allowed to vary freely, subject possibly to BX = 0.

Let [zeta](t), [eta](t) be continuously differentiable Gaussian processes with mean zero, unit variance, and common covariance function r(t), and such that [zeta](t) and [eta](t) are independent for all t, and consider the movements of a particle with time-varying coordinates ([zeta](t),...

Spatially homogeneous random evolutions arise in the study of the growth of a population in a spatially homogeneous random environment. The random evolution is obtained as the solution of a bilinear stochastic evolution equation. The main results are concerned with the asymptotic behavior of the...

Let X = (X1, X2,..., Xn) be a random vector in Rn (Euclidean n-space) with density f(x). X or f(x) is said to be multivariate reverse rule of order 2 (MRR2) if f(x [curly logical or] y) f(x [curly logical and] y) = f(x) f(y) where the lattice operations x [curly logical and] y and x [curly...

A function f(x) defined on = 1 - 2 - ... - n where each i is totally ordered satisfying f(x [logical or] y) f(x [logical and] y) = f(x) f(y), where the lattice operations [logical or] and [logical and] refer to the usual ordering on , is said to be multivariate totally positive of order 2...

The criterion robustness of the standard likelihood ratio test (LRT) under the multivariate normal regression model and also the inference robustness of the same test under the univariate set up are established for certain nonnormal distributions of errors. Restricting attention to the normal...

By employing fundamental results from "geometric" functional analysis and the theory of multifunctions we formulate a general model for (nonsequential) statistical decision theory, which extends Wald's classical model. From central results that hold for the model we derive a general theorem on...

Consider p independent distributions each belonging to the one parameter exponential family with distribution functions absolutely continuous with respect to Lebesgue measure. For estimating the natural parameter vector with p = p0 (p0 is typically 2 or 3), a general class of estimators...