The <Emphasis FontCategory="NonProportional">RngStreams software package provides one viable solution to the problem of creating independent random number streams for simulations in parallel processing environments. Techniques are presented for effectively using <Emphasis FontCategory="NonProportional">RngStreams with <Emphasis FontCategory="NonProportional">C++ programs that are parallelized via <Emphasis FontCategory="NonProportional">OpenMP or <Emphasis FontCategory="NonProportional">MPI. Ways...</emphasis></emphasis></emphasis></emphasis></emphasis>

We give a necessary and sufficient condition for a d-dimensional Lévy process to be in the matrix normalized domain of attraction of a d-dimensional normal random vector, as t↓0. This transfers to the Lévy case classical results of Feller, Khinchin, Lévy and Hahn and Klass for random walks....

We apply recent results on local U-statistics to obtain uniform in bandwidth consistency and central limit theorems for some commonly used estimators of integral functionals of density functions. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2008.

The estimated weighted empirical quantile process is introduced, and under mild regularity conditions is shown to converge weakly in L2(0, 1) to a Gaussian process. This leads to an elementary approach to the derivation of the asymptotic null distribution of Cramér-von Mises type statistics for...

One and two sample rank statistics are shown in general to be more efficient in the Bahadur sense than their sequential rank statistic analogues as defined by Mason (1981, Ann. Statist.9 424-436) and Lombard (1981, South African Statist. J.15 129-152), even though the two families of statistics...

Let [alpha]n and un be the uniform empirical and quantile processes. We investigate the asymptotic distribution of the suprema of [alpha]n(s)/(s(1 - s))1/2±[nu] and un(s)/(s(1 - s))1/2±[nu] with , when the supremum is taken over ranges, depending on n, in the middle of the interval [0, 1],...

Let Gn denote the empirical distribution based on n independent uniform (0, 1) random variables. The asymptotic distribution of the supremum of weighted discrepancies between Gn(u) and u of the forms ||wv(u)Dn(u)|| and ||wv(Gn(u))Dn(u)||, where Dn(u) = Gn(u)-u, wv(u) = (u(1-u))-1+v and 0...

Let X1,n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn,n be the order statistics of n independent random variables with a common distribution function F and let kn be positive numbers such that kn -- [infinity] and . With suitable centering and norming, we investigate the weak...