In this talk, results about the local asymptotic behavior of tests for the hypothesis of multivariate independence are presented. All considered procedures are functionals of the so-called empirical copula process, whose asymptotic law under contiguous alternatives is obtained. This result enables to compute, under many local dependence scenarios based on copulas, the local power curves as well as a natural extension to Pitman's asymptotic relative efficiency for many tests. Some Cramér-von Mises type procedures proposed by Deheuvels (1981) and Genest & Rémillard (2004) will be studied in more details.
Group for Research in Decision Analysis