Treated in this paper is the problem of estimating with squared error loss the generalized variance [Sigma] from a Wishart random matrix S: p - p ~ Wp(n, [Sigma]) and an independent normal random matrix X: p - k ~ N([xi], [Sigma] [circle times operator] Ik) with [xi](p - k) unknown. Denote the...

Basic results on stochastic differential equations in Hilbert and Banach space, linear stochastic evolution equations and some classes of nonlinear stochastic evolution equations are reviewed. The emphasis is on equations relevant to the study of spacetime stochastic processes. In particular the...

In the general Gauss-Markoff model (Y, X[beta], [sigma]2V), when V is singular, there exist linear functions of Y which vanish with probability 1 imposing some restrictions on Y as well as on the unknown [beta]. In all earlier work on linear estimation, representations of best-linear unbiased...

Let (X, ) be a measurable space, [Theta] [subset, double equals] an open interval and P[Omega] [short parallel] , [Omega] [epsilon] [Theta], a family of probability measures fulfilling certain regularity conditions. Let [Omega]n be the maximum likelihood estimate for the sample size n. Let...

A direct proof of a recent factorization theorem of Rozanov is given using the comparison theorem of D. Lowdenslager.

The distribution of the radius of convergence r([omega]) of a random power series with nonidentically distributed coefficients is considered. The results obtained here extend the well-known work in the identically distributed case.

Continuing an earlier work [4], properties of canonical Wiener processes are investigated. An analog of the sample path continuity property is obtained. A noncommutative counterpart of weak convergence is formulated. Operator processes (Pn, Qn) analogous to the random-walk approximating...

In this paper we give a unified derivation of the likelihood ratio (LR) statistics for testing the hypothesis on the dimensionality of regression coefficients under a usual MANOVA model. We also derive the LR statistics under a general MANOVA model and study their asymptotic null and nonnull...

In this paper, the authors derived exact expressions for the joint marginal densities of any few consecutive ordered roots of a class of random matrices which includes Wishart matrix, MANOVA matrix, and canonical correlation matrix. In addition, the authors obtained an exact expression for the...

The following path properties of real separable Gaussian processes [xi] with parameter set an arbitrary interval are established. At every fixed point the paths of [xi] are continuous, or differentiable, with probability zero or one. If [xi] is measurable, then with probability one its paths...