ASYMPTOTICS OF MULTIVARIATE RANDOMNESS STATISTICS

Kiefer considered the asymptotics of g-sample Cramer-Von Mises statist ics for a fixed q and sample sizes tending to infinity. For univariate observations, McDonald proved the asymptotic normality of these stati stics when q goes to infinity while the sample sizes stay fixed, Here we define a class of multivariate randomness statistics that generaliz es the class considered by McDonald. We also prove the asymptotic norm ality of such statistics when the sample sizes stay fixed while q tend s to infinity. (C) 1995 Academic Press, Inc.