2014/11/21 by Axel Bücher, Bücher, Axel, Betina Berghaus +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F17 #62G30 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability and Risk Models #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:60F17 #msc:62G30 #stat.TH
paper · pdf · doi:10.48550/arxiv.1411.5888
39 pages + 7 pages of supplementary material, 1 figure
arxiv created 2014/11/21 · openalex publication_date 2014/11/21 · arxiv updated 2014/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.