Fast and robust bootstrap method for testing hypotheses in the ICA model

摘要

Independent component analysis (ICA) is a widely used technique for extracting latent (unobserved) source signals from observed multidimensional measurements. In this paper we construct a fast and robust bootstrap (FRB) method for testing hypotheses on elements of the mixing matrix in the ICA model. The FRB method can be devised for estimators which are solutions to fixed-point (FP) equations. In this paper we develop FRB test for the widely popular FastICA estimator. The developed test can be used in real-world ICA analysis of high-dimensional data sets seen e.g. in big data analysis, as it avoids the common obstacles of conventional bootstrap such as immense computational cost and lack of robustness. Moreover, instability and convergence problems of the Fast ICA algorithm when applied to bootstrap data are prevented. Simulations and examples illustrate the usefulness and validity of the developed test.