This paper investigates the estimation of covariance matrices in multivariate mixed models. Some sufficient conditions are derived for a multivariate quadratic form and a linear combination of multivariate quadratic forms to be the BQUE (quadratic unbiased and severally minimum varianced)...

A method to construct the Wold decomposition for multivariate stationary stochastic processes xk, k [set membership, variant] Z, is presented. The method is based on orthogonal decompositions for xk, k [set membership, variant] Z, obtained by forming orthogonal projections of xk, k [set...

Mixtures of two beta or gamma distributions having given first four, three, or two moments are found and applied to tabulate to three decimals critical values of the locally most powerful criterion of sphericity or proportions of moments of order two of a p-variate normal distribution....

It is shown that the probability that a suitably standardized asymptotic maximum likelihood estimator of a vector parameter (i.e., an estimator which approximates the solution of the likelihood equation in a reasonably good way) lies in a measurable convex set can be approximated by an integral...

For continuous observations from time-sequential studies, suitable Cramér-von Mises and Kolmogorov-Smirnov types of (nonparametric) statistics (based on linear rank statistics) for testing hypotheses on some multiple-regression models are proposed and studied. The asymptotic theory of these...

General functional equations of the type [summation operator][phi]i(Ai't+Bi'u)=Ca(ut)+Db(tu)+Pk(t,u) and [Sigma][phi]i(Ci't) = Pk(t) have been solved, where Pk represents a polynomial of degree k in all the arguments, Cn(u [short parallel] t), a polynomial of degree a in u given t, and Db(t...

An explicit formula is obtained for the nonlinear predictor of Y(t) = X(t)2 - E(X(t)2), where X(t) is an N-ple Gaussian Markov process.

Measurable linear transformations from an abstract Wiener space to a Hilbert space are characterized. It is shown that the measure on any infinite dimensional abstract Wiener space can be transformed to that on any other by a measurable linear transformation.

Let X be an observation from a p-variate (p = 3) normal random vector with unknown mean vector [theta] and known covariance matrix . The problem of improving upon the usual estimator of [theta], [delta]0(X) = X, is considered. An approach is developed which can lead to improved estimators,...