Let FX,Y(x,y) be a bivariate distribution function and Pn(x), Qm(y), n, m = 0, 1, 2,..., the orthonormal polynomials of the two marginal distributions FX(x) and FY(y), respectively. Some necessary conditions are derived for the co-efficients cn, n = 0, 1, 2,..., if the conditional expectation...

[9] established multidimensional functional limit theorems for generalized U-statistics for estimable parameters which are stationary of order zero (the nondegenerate case). Similar univariate and bivariate functional limit theorems are derived for U-statistics in the degenerate case. The latter...

Tyan and Thomas (J. Multivariate Anal. 5 (1975), 227-235), have given a characterization of a class of bivariate distributions which yields, as a special case, a characterization of a class of bivariate Poisson distributions. In this paper we develop an analogous characterization of a class of...

Let [X, v, Y] be an abstract information channel with the input X = (X, ) and the output Y = (Y, ) which are measurable spaces, and denote by L(Y) = L(Y, ) the Banach space of all bounded signed measures with finite total variation as norm. The channel distribution [nu](·,·) is considered...

Consider a generalized random variable X assuming values in a Banach space 4 with conjugate space 4*. For separable or reflexive 4 the measurability, probability distribution, and other properties of X are characterized in terms of a collection of real random variables {a*(X) : a* [set...

Necessary and sufficient conditions are presented for jointly symmetric stable random vectors to be independent and for a regression involving symmetric stable random variables to be linear. The notion of n-fold dependence is introduced for symmetric stable random variables, and under this...

We extend the notion of real-valued asymptotic martingales to the Banach lattice valued case. Unlike the other extensions, the notion of "orderamart" preserves the lattice property of real amarts. We show also, a Riesz decomposition, a weak and strong convergence theorem, a probabilistic...

The joint asymptotic multinormality of certain linear signed-rank statistics introduced by Shane and Puri (1969) is established for the nonidentically distributed case; moreover, the usual restriction forbidding constant score generating functions is dropped. In addition, sufficient conditions...

Distribution-free tests for permutational symmetry of correlated variables have been offered recently in the literature. However, situations arise when all the planned measurements are available only on some subjects, while others drop out at various stages of the experiment. The present paper...

Let [alpha](n1, n2) be the probability of classifying an observation from population [Pi]1 into population [Pi]2 using Fisher's linear discriminant function based on samples of size n1 and n2. A standard estimator of [alpha], denoted by T1, is the proportion of observations in the first sample...