Weak convergence of the weighted empirical beta copula process

JOURNAL OF MULTIVARIATE ANALYSIS

卷:166

Article

Berghaus, Betina¹  Segers, Johan² 

[1] Ruhr Univ Bochum, Fak Math, Univ Str 150, D-44780 Bochum, Germany

[2] Catholic Univ Louvain, ISBA, Voie Roman Pays 20, B-1348 Louvain La Neuve, Belgium

关键词: Copula;    Empirical beta copula;    Empirical copula;    Pickands dependence function;    Weighted weak convergence;   

DOI  :  10.1016/j.jmva.2018.03.009

来源: Elsevier

【 摘 要 】

The empirical copula has proved to be useful in the construction and understanding of many statistical procedures related to dependence within random vectors. The empirical beta copula is a smoothed version of the empirical copula that enjoys better finite-sample properties. At the core lie fundamental results on the weak convergence of the empirical copula and empirical beta copula processes. Their scope of application can be increased by considering weighted versions of these processes. In this paper we show weak convergence for the weighted empirical beta copula process. The weak convergence result for the weighted empirical beta copula process is stronger than the one for the empirical copula and its use is more straightforward. The simplicity of its application is illustrated for weighted Cramer-von Mises tests for independence and for the estimation of the Pickands dependence function of an extreme-value copula. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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