Towards upper bounding the variance of the demixing estimate of a geometry based Independent Component Analysis algorithm - Technical Report

For the Independent Component Analysis(ICA) algorithm (using a geometric approach) given in [1], we provide a probabilistic upper bound on the Euclidean error of constituents of the demixing matrix estimate resulting from unmixed input, under the condition that the algorithm converges to the global optimum, and derive an asymptotic bound on the expected squared error for large sample sizes from it. This error bound is found to be of order $O(N^{-2 + 2beta})$, where $N$ is the sample size and $beta in (0,1)$ is chosen arbitrarily. The result can be used to establish the asymptotic behaviour of the variance of the demixing matrix estimate for arbitrarily linearly mixed independent inputs.