It is shown that the analytical characterizations of q-variate interpolable and minimal stationary processes obtained by H. Salehi (Ark. Mat., 7 (1967), 305-311; Ark. Mat., 8 (1968), 1-6; J. Math. Anal. Appl., 25 (1969), 653-662), and later by A. Weron (Studia Math., 49 (1974), 165-183), can be...

Let X1, X2,..., Xn be identically distributed possibly dependent random variables with finite pth absolute moment assumed without loss of generality to be equal to 1. Denote the order statistics by X1:n, X2:n,..., Xn:n. Bounds are derived for E(Xn:n) when it is assumed that the Xi's are (i)...

Measures with values in a countably order-complete vector lattice are considered. The underlying [sigma]-algebra is assumed to be [sigma]-isomorphic to the Borel sets of the real line. Given one such measure, densities are searched which are not necessarily scalar-valued for smaller measures....

Under weak regularity conditions of the covariance sequence, it is shown that the joint limiting distribution of the maxima on each coordinate of a stationary Gaussian multivariate sequence is that of independent random variables with marginal Gumbel distributions.

Likelihood ratio tests are derived for testing the structure of mean values in a two-way classification. The most general hypothesis considered is when the mean values are subject to row and column effects and interaction has a given complexity. The observations corresponding to a row or a...

Some partial orderings of positively dependent exchangeable random variables are introduced. The interrelations among them, the inequalities which follow from them and two models which yield such partial orderings are then discussed. Particular examples include ordering multivariate normal, t,...

A new approach to the asymptotic normality of the multivariate linear rank statistics is provided along with the Berry-Esséen and the Prohorov distance estimates for the remainder term in the convergence to normality.

This second part of the work on Banach space valued multifunctions begins with a detailed study of set valued martingales, which have their values in a Banach space. Several new convergence theorems are established for different modes of convergence. The profile of a multifunction in connection...

In this note, the authors propose a new nonparametric method of estimation of density using orthonormal systems iteratively. The asymptotic mean integrated square error of the estimate at each stage is less than or equal to that of the preceding stage. The new estimate is better, in some cases,...

Let (X, , P) be a probability space and n, n = 1, a sequence of classes of measurable complex-valued functions on (X, , P). Under a weak metric entropy condition on n and sup {||g||[infinity]: g [set membership, variant] n}, Glivenko-Cantelli theorems are established for the classes n with...