The present paper contains assertions on asymptotic distributions of statistics used for the nonparametric multivariate testing symmetry. The results are proved under the hypothesis of symmetry H1, the near alternative and the general alternative. The proofs of the main theorems (Theorems 2.3,...

This paper derives a sharp bound for the probability that a sum of independent symmetric random vectors lies in a symmetric convex set. In one dimension this bound is an improvement of an inequality first proved by Kolmogorov. The subject of multidimensional concentration functions is also treated.

The basic result of the paper states: Let F1, ..., Fn, F1',..., Fn' have proportional hazard functions with [lambda]1 ,..., [lambda]n , [lambda]1' ,..., [lambda]n' as the constants of proportionality. Let X(1) = ... = X(n) (X(1)' = ... = X(n)') be the order statistics in a sample of size n from...

Asymptotic expansions, valid for large error degrees of freedom, are given for the multivariate noncentral F distribution and for the distribution of latent roots in MANOVA and discriminant analysis. The asymptotic results are expressed in terms of elementary functions which are easy to compute...

The notion of continuity for continuous-time information sources which was introduced by Pinsker has found numerous applications in information theory. Continuity in probability is an important concept in the theory of continuous-time stochastic processes. It is shown that these two forms of...

For a simple multivariate regression model, nonparametric estimation of the (vector of) intercept following a preliminary test on the regression vector is considered. Along with the asymptotic distribution of these estimators, their asymptotic bias and dispersion matrices are studied and allied...

Bivariate stable distributions are defined as those having a domain of attraction, where vectors are used for normalization. These distributions are identified and their domains of attraction are given in a number of equivalent forms. In one case, marginal convergence implies joint convergence....

An algorithm is presented for the numerical evaluation of the null distribution of the largest latent root of a beta matrix, based on a finite series recently given by Khatri [6]. The same method can also be used for the distribution of the smallest latent root, and it can be easily adapted to...

Let B be the noncentral beta matrix defined by B = (Sh + Se)-1/2 · Sh(Se + Sh)-1/2, where Se and Sh are independently distributed as Wishart distribution Wp(r, [Sigma]) and noncentral Wishart distribution Wp(q, [Sigma], [Omega]), respectively. Then asymptotic expansions of the distributions...

Let {} denote the N-parameter Wiener process on . For multiple sequences of certain independent random variables the authors find lower bounds for the distributions of maximum of partial sums of these random variables, and as a consequence a useful upper bound for the yet unknown function , c =...