K-Sample Test for Equality of Copulas

Comparaison Simultanée de $K\geq 2$ Copules Multivariées

Yves Ismaël Ngounou Bakam (1) , Denys Pommmeret (1, 2)

1 I2M - Institut de Mathématiques de Marseille
2 LSAF - Laboratoire de Sciences Actuarielles et Financières [Lyon]

We propose a test procedure to compare simultaneously K copulas, with K ≥ 2. The K observed populations can be paired. The test statistic is based on the differences between orthogonal projection coefficients associated to the density copulas, that we called copula coefficients. The procedure is data driven and we obtain a chi-square asymptotic distribution of the test statistic under the null. We illustrate our procedure via numerical studies and through two real datasets. Eventually, a clustering algorithm is deduced from the Ksample test and its performances are illustrated in a simulation experiment.

Keywords: MSC2020 subject classifications: Primary 62H05; secondary 62H15 Clustering; copula coefficients; data driven; Legendre polynomials

Domains: Statistics [stat]; Methodology [stat.ME]; Statistics [stat]; Applications [stat.AP]; Statistics [stat]; Statistics Theory [stat.TH]

Yves Ismaël Ngounou Bakam, Denys Pommmeret. K-Sample Test for Equality of Copulas. 2022. ⟨hal-03475324v2⟩