It is shown that every full eA decomposable probability measure on Rk, where A is a linear operator all of whose eigenvalues have negative real part, is either absolutely continuous with respect to Lebesgue measure or continuous singular with respect to Lebesgue measure. This result is used to...

We consider the problem of constructing entrance laws for Feller diffusions on the state space (0, [infinity]). Our method, based on Feller-McKean theory of one-dimensional diffusions, gives an analytic expression for the entrance density in terms of transition density. Moreover, the entrance...

A random vector is said to have a 1-symmetric distribution if its characteristic function is of the form [phi](t1 + ... + tn). 1-Symmetric distributions are characterized through representations of the admissible functions [phi] and through stochastic representations of the radom vectors, and...

Multivariate integral kernel transformations of the multivariate empirical process are considered. The asymptotic behaviour of these transforms are investigated when a null-hypothesis completely specifies the underlying distribution and also when parameters are also estimated from the sample. In...

The spectral distribution of a central multivariate F matrix is shown to tend to a limit distribution in probability under certain conditions as the number of variables and the degrees of freedom tend to infinity.

Some types of density estimators, particularly those based on trigonometric series, converge reasonably quickly to their limit except in the neighbourhood of one or two singularities. In this situation the mean integrated square error, the traditional measure of the efficiency of a density...

Let Y1,..., Yn be independent identically distributed random variables with distribution function F(x, [theta]), [theta] = ([theta]'1, [theta]'2), where [theta]i (i = 1, 2) is a vector of pi components, p = p1 + p2 and for [for all][theta][set membership, variant]I, an open interval in p, F(x,...

In the present paper it is shown that the central limit theorem holds for some non-linear functionals of stationary Gaussian fields if the correlation function of the underlying field tends fast enough to zero. The results are formulated in terms of the Hermite rank of the functional and of the...

Herman Chernoff used Hermite polynomials to prove an inequality for the normal distribution. This inequality is useful in solving a variation of the classical isoperimetric problem which, in turn, is relevant to data compression in the theory of element identification. As the inequality is of...

A point estimator based on minimization of the rank analogue of the Cramér-von Mises statistic is proposed for the slope parameter [beta] in the simple linear regression model. The asymptotic distribution of the estimator is derived and its variance is compared to the asymptotic variances of...