Tests of Multivariate Independence Based on Copula

Abstract

Very often the aim of statistical analysis is to identify dependencies among variables. More and more multidimensional variables and processes are in focus. This paper presents the tests of multivariate independence based on the empirical copula and the Möbius transform. The important contribution to the development of this test had works of Blum, Kiefer, Rosenblatt (1961), Dugue (1975), Deheuvels (1981), Ghoudi, Kulperger, Remillard (2001), Genest, Rémillard (2004) and Kojadinovic, Holmes (2009). The first section of the article presents the copula function and the empirical copula. The next section introduces the multivariate independence tests and the last section gives the empirical example.