An asymptotic expansion of the joint distribution of k largest characteristic roots CM(i)(SiS0-1), i = 1,..., k, is given, where S'is and S0 are independent Wishart matrices with common covariance matrix [Sigma]. The modified second-approximation procedure to the upper percentage points of the...

In the last paper, the geometry of the Sz.-Nagy-Foias model for contraction operators on Hilbert spaces was used to advantage in several problems of multivariate analysis. The lifting of intertwining operators, one of the basic results from the Sz.-Nagy-Foias theory, is now recognized as the...

An asymptotic expansion for large sample size n is derived by a partial differential equation method, up to and including the term of order n-2, for the 0F0 function with two argument matrices which arise in the joint density function of the latent roots of the covariance matrix, when some of...

Unique solutions are shown to exist for systems of stochastic integral equations which allow right-continuous semimartingales (also known as quasimartingales) as differentials.

Define coefficients (?[lambda]) by C[lambda](Ip + Z)/C[lambda](Ip) = [Sigma]k=0l [Sigma][varkappa][set membership, variant]k ([varkappa][lambda]) C?(Z)/C?(Ip), where the C[lambda]'s are zonal polynomials in p by p matrices. It is shown that C[varkappa](Z) etr(Z)/k! = [Sigma]l=k[infinity]...

Let ([Omega], [Sigma], P) be a fixed complete probability space, the real Schwartz space, and its strong dual. and are partially ordered by and respectively, where is the positive cone of nonnegative functions in and its dual in . is a strict -cone and is normal, where is the family of all...

Three methods of estimating the parameters of a power spectrum are analyzed. The three methods are shown to give consistent and, under certain conditions, asymptotically equivalent results. However, one method, based on an approximate likelihood analysis, is seen to be superior to the other two...

This paper contains the following three types of results: First, a 1-1 correspondence is established between Gaussian measures on Lp, 1 = p [infinity], and Gaussian processes with paths in Lp. Second, a 0-1 law for Gaussian measures on Fréchet spaces is proved, which is subsequently applied to...

In this paper, it is shown that the distribution of the spectrum of A + X gives (essentially) a complete set of orthogonal invariants for the (real nonsymmetric) matrix A.