Asymptotics of Multivariate Randomness Statistics

Kiefer considered the asymptotics of q-sample Cramer-von Mises statistics for a fixed q and sample sizes tending to infinity. For univariate observations, McDonald proved the asymptotic normality of these statistics when q goes to infinity while the sample sizes stay fixed. Here we define a class of multivariate randomness statistics that generalizes the class considered by McDonald. We also prove the asymptotic normality of such statistics when the sample sizes stay fixed while q tends to infinity.

Weighted-Symmetry Tests

Weighted-symmetry is an extension of the classical notion of symmetry in which the left and right probability tails are similar under a scaling transformation. The aim of this paper is to develop tests of weighted-symmetry based on some empirical processes. It is shown that the limiting distributions of these processes are Brownian bridges or Brownian motions. Moreover, it is proved that the HodgesLehmann estimators for the main parameters, based on a generalization of the Wilcoxon signed rank test, are asymptotically Gaussian. Key words: Weighted-symmetry; Pseudo-observations; Wilcoxon signed rank test. ? The authors are supported in part by the Fonds Institutionnel de Recherche, Universit'e du Qu'ebec `a Trois-Rivi`eres, the Fonds pour la formation de chercheurs et l'aide `a la recherche du Gouvernement du Qu'ebec and by the Natural Sciences and Engineering Research Council of Canada. Preprint submitted to Elsevier Preprint 1 Introduction Testing whether a set of data is drawn fro..

Test of independence and randomness based on the empirical copula process

Copula, Cramér-von Mises statistic, empirical process, Möbius inversion formula, pseudo-observations, semi-parametric models, serial dependence, tesis of independence, 60F05, 2E20,