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Third and Fourth Cumulants in Independent Component Analysis

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The independent component model is a latent variable model where the components of the observed random vectors are linear combination of latent independent variables. The aim is then to find an estimate for a transformation matrix back to independent components. In this talk, we consider the joint use of third and fourth cumulants in finding independent components. First, univariate cumulants are used as projection indices in search for independent components (projection pursuit). Second, multivariate cumulant matrices are jointly used to solve the problem. The properties of the estimates are considered in detail through corresponding optimization problems, estimating equations, algorithms and asymptotic statistical properties. Comparisons of the asymptotic variances of the estimates in wide independent component models show that in most cases projection pursuit approach using both third and fourth scared cumulants is a safe choice.

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