Abstract
Independent component analysis (ICA) solves the blind source separation problem by evaluating higher-order statistics, e.g. by estimating fourth-order moments. While estimation errors of the kurtosis can be shown to asymptotically decay with sample size according to a square-root law, they are subject to two further effects for finite samples. Firstly, errors in the estimation of kurtosis increase with the deviation from Gaussianity. Secondly, errors in kurtosis-based ICA algorithms increase when approaching the Gaussian case. These considerations allow us to derive a strict lower bound for the sample size to achieve a given separation quality, which we study analytically for a specific family of distributions and a particular algorithm (fastICA). We further provide results from simulations that support the relevance of the analytical results.
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Herrmann, J.M., Theis, F.J. (2007). Statistical Analysis of Sample-Size Effects in ICA. In: Yin, H., Tino, P., Corchado, E., Byrne, W., Yao, X. (eds) Intelligent Data Engineering and Automated Learning - IDEAL 2007. IDEAL 2007. Lecture Notes in Computer Science, vol 4881. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77226-2_43
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DOI: https://doi.org/10.1007/978-3-540-77226-2_43
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