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.
The authors are grateful to D. Erdogmus for having inspirited this work by fruitful discussion on expectation and variance of cdf differences and m-spacings.
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Vrins, F., Verleysen, M. (2006). Minimum Support ICA Using Order Statistics. Part I: Quasi-range Based Support Estimation. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2006. Lecture Notes in Computer Science, vol 3889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11679363_33
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DOI: https://doi.org/10.1007/11679363_33
Publisher Name: Springer, Berlin, Heidelberg
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