Testing independence using C -power functions

Testing independence within a random vector is a fundamental task in statistical analysis, underpinning numerous applications across scientific domains. With the increasing prominence of copulas in capturing dependence structures, copula-based independence tests have received considerable attention. This study introduces a novel Cramér-von Mises test statistic based on C-power functions, constructed to detect deviations from independence among components of a continuous random vector. The asymptotic distribution of the test statistic is established under the null hypothesis as well as under a sequence of local alternatives. Evidence from simulation studies and real data applications suggests that the proposed test often achieves competitive or higher power than the empirical copula-based test, particularly in detecting complex or subtle forms of dependence.