Fourth Moments and Independent Component Analysis

By Jari Miettinen, Sara Taskinen, Klaus Nordhausen, Hannu Oja. 2014

85 citations recorded by the source corpus.

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.

Subfields: Computational Mathematics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/cac09f874e69f8af529b99fe70e970b1789de3cf

Citations in the corpus

• GMM Estimation of Non-Gaussian Structural Vector Autoregression (2019, unknown): “Moreover, the procedures are typically seen as algorithms rather than estimators, and their statistical properties are not necessarily known (see Miettinen et al. 2015) for a statistical analysis of several of these procedures).”