An n-dimensional random vector X is said (Cambanis, S., Keener, R., and Simons, G. (1983). J. Multivar. Anal., 13 213-233) to have an [alpha]-symmetric distribution, [alpha] 0, if its characteristic function is of the form [phi]([xi]1[alpha] + ... + [xi]n[alpha]). Using the Radon transform,...

Let H be a Hilbert space and ([Omega], , [mu]) be a probability measure space. Consider the Hilbert space L02([Omega]; H) consisting of all H-valued strong random variables on [Omega] with zero mean which are square integrable with respect to [mu]. We study L02([Omega]; H)-valued processes over...

The exact density is given for the r-content of the simplicial convex hull of r + 1 independent points in n, each having a type II [beta] distribution. The density is given in the form of an integral of Mellin-Barnes type, which even in the most general cases can be evaluated to give a series...

Let r1 r2 ... be the sample canonical correlations in a sample of size n from a multivariate normal population partitioned into two subvectors with population canonical correlations [varrho]1 [varrho]2 .... Let one of the subvectors be augmented by adding one or more variables to it. For the...

The limiting (as the significance level approaches 0) Pitman efficiency of a new "regression-based" rank test of independence to Kendall's tau and Spearman's rho is derived. The result is based on a version of [17], Ann. Statist.4 1003-1011) on coincidence of the limiting Pitman efficiency and...

Learn-merge invariance is a property of prior distributions (related to postulates introduced by the philosophers W. E. Johnson and R. Carnap) which is defined and discussed within the Bayesian learning model. It is shown that this property in its strong formulation characterizes the Dirichlet...

Let ? be a functional defined on a family of probability measures , containing a subfamily . The paper presents a condition involving the gradient of the functional under which--for probability measures in --"adaptation" is possible, i.e., under which the asymptotic variance bound for estimators...

This paper treats some 2-dimensional zero-mean stationary Gaussian processes with some long-range dependence and gives the limit theorems for the time spent by those processes in some domains in R2 as an application of the non-central limit theorem.

In this article we study the behaviour of translation invariant experiments. The main result establishes necessary and sufficient conditions for the local approximation of a sequence of suitably normalized product experiments by Gaussian shifts with respect to the weak convergence. Moreover, it...