A multivariate linear rank test of independence based on a multiparametric copula with cubic sections

This paper generalizes the locally optimal linear rank test based on copula from Shirahata (1974) resp. Guillén and Isabel (1998) and Genest et al. (2006) to p dimensions and introduces a new X2-type test for global independence (Nelsen test). The test is compared to similar nonparametric tests by means of the power under several alternatives and sample sizes. However, the actual strength of the Nelsen test is the fast examination of a test decision due to the closed form expression of the asymptotic distribution of the test statistic which is provided by this paper.