On testing hypotheses of mixing vectors in the ICA model using fastica

Independent component analysis (ICA) is a widely used multivariate analysis technique with applications in many diverse fields such as medical imaging, image processing and data mining. Up to date almost all ICA research have focused on estimation of the mixing and demixing matrix but almost nothing exists on testing hypotheses of the mixing vectors or mixing coefficients. In this paper, we construct tests for this purposes using deflation-based FastICA estimator. The developed (Wald-type) test statistic utilizes the asymptotic covariance matrix of the estimator and its asymptotic normality. The developed test can be used e.g. in fMRI analysis where the mixing vectors correspond to the time courses of the independent spatial maps. In this context, it is of interest to test if the hypothesized task-related time course is significantly different from the found mixing vectors. Simulations and an example on synthetic data illustrate the validity and usefulness of our approach.