  We propose a class of flexible non-parametric tests for the presence of
dependence between components of a random vector based on weighted
Cram\'{e}r-von Mises functionals of the empirical copula process. The weights
act as a tuning parameter and are shown to significantly influence the power of
the test, making it more sensitive to different types of dependence. Asymptotic
properties of the test are stated in the general case, for an arbitrary bounded
and integrable weighting function, and computational formulas for a number of
weighted statistics are provided. Several issues relating to the choice of the
weights are discussed, and a simulation study is conducted to investigate the
power of the test under a variety of dependence alternatives. The greatest gain
in power is found to occur when weights are set proportional to true deviations
from independence copula.
