Weak convergence of the empirical copula process with respect to weighted metrics
Loading...
Date
2014
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The empirical copula process plays a central role in the asymptotic
analysis of many statistical procedures which are based on copulas
or ranks. Among other applications, results regarding its weak convergence
can be used to develop asymptotic theory for estimators of
dependence measures or copula densities, they allow to derive tests for
stochastic independence or specific copula structures, or they may serve
as a fundamental tool for the analysis of multivariate rank statistics.
In the present paper, we establish weak convergence of the empirical
copula process (for observations that are allowed to be serially dependent)
with respect to weighted supremum distances. The usefulness
of our results is illustrated by applications to general bivariate rank
statistics and to estimation procedures for the Pickands dependence
function arising in multivariate extreme-value theory.
Description
Table of contents
Keywords
empirical copula process, Pickands dependence function, bivariate rank statistics, strongly mixing, weighted weak convergence