  Independent component analysis (ICA) decomposes multivariate data into
mutually independent components (ICs). The ICA model is subject to a constraint
that at most one of these components is Gaussian, which is required for model
identifiability. Linear non-Gaussian component analysis (LNGCA) generalizes the
ICA model to a linear latent factor model with any number of both non-Gaussian
components (signals) and Gaussian components (noise), where observations are
linear combinations of independent components. Although the individual Gaussian
components are not identifiable, the Gaussian subspace is identifiable. We
introduce an estimator along with its optimization approach in which
non-Gaussian and Gaussian components are estimated simultaneously, maximizing
the discrepancy of each non-Gaussian component from Gaussianity while
minimizing the discrepancy of each Gaussian component from Gaussianity. When
the number of non-Gaussian components is unknown, we develop a statistical test
to determine it based on resampling and the discrepancy of estimated
components. Through a variety of simulation studies, we demonstrate the
improvements of our estimator over competing estimators, and we illustrate the
effectiveness of the test to determine the number of non-Gaussian components.
Further, we apply our method to real data examples and demonstrate its
practical value.
