Minimum support ICA using order statistics. Part I: Quasi-range based support estimation

Abstract

The minimum support ICA algorithms currently use the extreme statistics difference (also called the statistical range) for support width estimation. In this paper, we extend this method by analyzing the use of (possibly averaged) differences between the N -m + 1-th and m-th order statistics, where N is the sample size and m is a positive integer lower than N/2. Numerical results illustrate the expectation and variance of the estimators for various densities and sample sizes; theoretical results are provided for uniform densities. The estimators are analyzed from the specific viewpoint of ICA, i.e. considering that the support widths and the pdf shapes vary with demixing matrix updates. © Springer-Verlag Berlin Heidelberg 2006.