Independent vector analysis, the Kotz distribution, and performance bounds

The recent extensions of independent component analysis (ICA) to exploit source dependence across multiple datasets, termed independent vector analysis (IVA), have thus far only considered two multivariate source distribution models: the Gaussian and a second-order uncorrelated Laplacian distribution. In this paper, we introduce the use of the Kotz distribution family as a more flexible source distribution model which exploits both second and higher-order statistics. The Cramér-Rao lower bound (CRLB) for IVA performance prediction is shown to be analogous to the bound for blind source separation (BSS). Lastly, we provide an analytic expression for the CRLB when the sources follow the multivariate power exponential (MPE) subclass of distributions within the Kotz family.