  In independent component analysis it is assumed that the components of the
observed random vector are linear combinations of latent independent random
variables, and the aim is then to find an estimate for a transformation matrix
back to these independent components. In the engineering literature, there are
several traditional estimation procedures based on the use of fourth moments,
such as FOBI (fourth order blind identification), JADE (joint approximate
diagonalization of eigenmatrices), and FastICA, but the statistical properties
of these estimates are not well known. In this paper various independent
component functionals based on the fourth moments are discussed in detail,
starting with the corresponding optimization problems, deriving the estimating
equations and estimation algorithms, and finding asymptotic statistical
properties of the estimates. Comparisons of the asymptotic variances of the
estimates in wide independent component models show that in most cases JADE and
the symmetric version of FastICA perform better than their competitors.
