Let be a nonparametric estimate of a two-dimensional density f(x,y) constructed with the help of two-dimensional "window." The main purpose of the paper is to study the asymptotic properties of the marginal moments estimates and differentiable functions , of these moments.

The existence of a Gaussian measure W on C([0, 1]2) with EW(x(s1,t1)·x(s2,t2))=min(s1,s2)·min(t1,t2) as its covariance function and an extension of Donsker's theorem for C([0, 1]2) are given.

Shanbag gave a characterization of the exponential and geometric distribution in terms of conditional expectations. Recently, Kotlarski generalized his method to obtain some properties of univariate probability distributions through conditional expectations. A property of bivariate distributions...

The aim of this paper is to examine multiple Markov dependence for the discrete as well as for the continuous parameter case. In both cases the Markov property with arbitrary parameter values is investigated and it is shown that it leads to the degeneration of the multiple Markov dependence to...

This paper analyzes the problem of using the sample covariance matrix to detect the presence of clustering in p-variate data in the special case when the component covariance matrices are known up to a constant multiplier. For the case of testing one population against a mixture of two...

The admissible values of the coefficient in a bivariate Eyraud-Gumbel-Morgenstern (EGM) distribution are found. For multivariate EGM distributions necessary and sufficient conditions are given for its coefficients, and its conditional distributions are found and shown to belong to a family of...

The generalized binomial coefficients (?[lambda]) are defined by , where the Ck(R) are the zonal polynomials of the m - m matrix R. In this paper some simple expressions are derived which allow straightforward calculation of a large number of these coefficients.

We show that an observer recording only the presence or absence of a Gaussian process in a window can reconstruct its correlation function.

Families of minimax estimators are found for the location parameters of a p-variate distribution of the form , where G(·) is a known c.d.f. on (0, [infinity]), p = 3 and the loss is sum of squared errors. The estimators are of the form (1 - ar(X'X)/E0(1/X'X)X'X)X where 0 = a = 2, r(X'X) is...

On the basis of a random sample of size n on an m-dimensional random vector X, this note proposes a class of estimators fn(p) of f(p), where f is a density of X w.r.t. a [sigma]-finite measure dominated by the Lebesgue measure on Rm, P = (p1,...,pm), pj = 0, fixed integers, and for x =...