Using our previous results we extend to the case of polynomial regression a recent characterization, obtained by Rao and Sinha, of the Dirichlet distributions. We also show that the class of distributions considered by Rao and Sinha possess many properties previously established by the authors...

The paper develops the spectral theory corresponding to the various time domain Wold decompositions of a discrete two-parameter stationary second-order random field (ssorf). Appropriate Szegö-type error formulas are established. Minimality and interpolability are defined for ssorf's and...

The discrete and continuous parameter forms of the mean ergodic theorem conclude that as N -- [infinity] or [tau] -- [infinity]. The ergodic limit P is shown to depend continuously on the operator T in the discrete case or on the infinitesimal generator A of the semigroup T in the continuous...

Let the distribution of a random vector X belong to the multidimensional exponential family. A Cacoullos-type, lower-bound, inequality for the variance of g(X) is given, which is shown to characterize the exponential family.

In this paper we introduce the concept of m(n)-decomposability as an alternative to classical mixing concepts. We illustrate how to handle the ensuing technicalities by proving asymptotic normality of L-statistics, based on such a decomposable time series, as a typical example.

Characterization problems of setwise independence are considered by introducing the setwise dependence class SMk(n). Two questions are answered: 1. (i) Under which conditions is a strongly positive orthant dependent random vector setwise independent.2. (ii) Under what kind of dependence...

This paper presents a Bayesian approach to empirical regression modeling in which the response function is represented by a power series expansion in Hermite polynomials. The common belief that terms of low degree will reasonably approximate the response function is reflected by assigning prior...

This paper deals with uniform rates of convergence for the empirical distribution function and the empirical characteristic function for a broad class of stationary linear processes. In particular, the class X(n) = [Sigma]i=0[infinity] [delta](i) z(n-1) is considered under the conditions that...

Let S be a p - p random matrix having a Wishart distribution Wp(n,n-1[Sigma]). For testing a general covariance structure [Sigma] = [Sigma]([xi]), we consider a class of test statistics Th = n inf [varrho]h(S, [Sigma]([xi])), where [varrho]h([Sigma]1, [Sigma]2) = [Sigma]j = 1ph([lambda]j) is a...

This paper shows an embedding of the manifold of multivariate normal densities with informative geometry into the manifold of definite positive matrices with the Siegel metric. This embedding allows us to obtain a general lower bound for the Rao distance, which is itself a distance, and we...