Based on an idea of Rosenblatt, the methods of interpolation theory are used to establish moment inequalities and equivalence relations for measures of dependence between two or more families of random variables. A couple of "interpolation" theorems proved here appear to be new.

Asymptotic expansions for a class of functional limit theorems are investigated. It is shown that the expansions in this class fit into a common scheme, defined by a sequence of functions hn ([var epsilon]1,..., [var epsilon]n), n = 1, of "weights" (for nobservations), which are smooth,...

For the multivariate linear model, coordinatewise M-estimators as well as an extension of the Maronna-type M-estimators are considered. Based on the Jurecková (asymptotic) linearity of M-statistics, the asymptotic distribution theory of the proposed estimators is studied under appropriate...

In this paper, an iterative estimate of the multivariate density is proposed when the variables are binary in nature. Some properties of this estimate are also discussed. Finally, applications of this estimate are discussed in the areas of pattern recognition and reliability.

It is shown that the positivity of the angle between the past and future of a multivariate stationary process is sufficient for the existence of a mean-convergent autoregressive series representation of its linear predictor. A large class of multivariate processes whose past and future are at...

Let X1, X2,..., be independent, identically distributed random variables. Suppose that the linear forms L1 = [Sigma]j=1[infinity]ajXj and L2 = [Sigma]j=1[infinity]bjXj exist with probability one and are identically distributed; necessary and sufficient conditions assuring that X1 is normally...

Cramér's inversion formula for the distribution of a quotient is generalized to matrix variates and applied to give an alternative derivation of the matrix t-distribution.

Banach space valued multifunctions defined on a complete [sigma]-finite measure space ([Omega], [Sigma], [mu]) are studied. Their set valued integral is defined and its properties are examined. Since the definition of the integral involves the set of integrable selectors of the multifunction,...

Let X be a p-dimensional random vector with density f(||X-[theta]||) where [theta] is an unknown location vector. For p = 3, conditions on f are given for which there exist minimax estimators [theta](X) satisfying ||Xt|| · ||[theta](X) - X|| = C, where C is a known constant depending on f....

Suppose the stationary r-dimensional multivariate time series {yt} is generated by an infinite autoregression. For lead times h=1, the linear prediction of yt+h based on yt, yt-1,... is considered using an autoregressive model of finite order k fitted to a realization of length T. Assuming that...