Open Access
2024 Smooth test for equality of copulas
Yves Ismaël Ngounou Bakam, Denys Pommeret
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Electron. J. Statist. 18(1): 895-941 (2024). DOI: 10.1214/24-EJS2220


A smooth test to simultaneously compare K copulas, where K2, is proposed. The K observed populations can be paired. The test statistic is based on the differences between moment sequences, called copula coefficients. These coefficients characterize the copulas, even in cases where the copula densities may not exist. The procedure involves a two-step data-driven procedure. In the initial step, the most significantly different coefficients are selected for all pairs of populations. The subsequent step utilizes these coefficients to identify populations that exhibit significant differences. To illustrate the efficacy of our method, we present numerical studies that demonstrate its performance. Furthermore, we apply our methodology, implemented in the “Kcop” R package, to two real datasets.


The authors would like to express their gratitude for the thorough reading, thoughtful comments, and numerous helpful suggestions provided by two anonymous referees and an Associate Editor. Their contributions greatly contributed to the improvement of this paper. The authors would like to extend special thanks to the Associate Editor for his helpful remarks, which led to Proposition 1. The second author would also like to acknowledge the support received from the Research Chair ACTIONS under the aegis of the Risk Foundation, an initiative by BNP Paribas Cardif and the Institute of Actuaries of France.


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Yves Ismaël Ngounou Bakam. Denys Pommeret. "Smooth test for equality of copulas." Electron. J. Statist. 18 (1) 895 - 941, 2024.


Received: 1 August 2022; Published: 2024
First available in Project Euclid: 26 February 2024

Digital Object Identifier: 10.1214/24-EJS2220

Keywords: Copula coefficients , data-driven smooth test , K-sample , Legendre polynomials

Vol.18 • No. 1 • 2024
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