  We propose a family of tests of the validity of the assumptions underlying
independent component analysis methods. The tests are formulated as L2-type
procedures based on characteristic functions and involve weights; a proper
choice of these weights and the estimation method for the mixing matrix yields
consistent and affine-invariant tests. Due to the complexity of the asymptotic
null distribution of the resulting test statistics, implementation is based on
permutational and resampling strategies. This leads to distribution-free
procedures regardless of whether these procedures are performed on the
estimated independent components themselves or the componentwise ranks of their
components. A Monte Carlo study involving various estimation methods for the
mixing matrix, various weights, and a competing test based on distance
covariance is conducted under the null hypothesis as well as under
alternatives. A real-data application demonstrates the practical utility and
effectiveness of the method.
