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This introduction to the R package ICS is a (slightly) modified version of Nordhausen, Oja, and Tyler (2008c), published in the Journal of Statistical Software. Invariant coordinate selection (ICS) has recently been introduced as a method for exploring multivariate data. It includes as a special case a method for recovering the unmixing matrix in… (More)

Description The package provides multivariate tests, estimates and methods based on the identity score, spatial sign score and spatial rank score. The methods include one and c-sample problems, shape estimation and testing, linear regression and principal components.

In the independent component (IC) model it is assumed that the components of the observed p-variate random vector x are linear combinations of the components of a latent p-vector z such that the p components of z are independent. Then x = Ωz where Ω is a full-rank p × p mixing matrix. In the independent component analysis (ICA) the aim is to estimate an… (More)

Deflation-based FastICA, where independent components (IC's) are extracted one-by-one, is among the most popular methods for estimating an unmixing matrix in the independent component analysis (ICA) model. In the literature, it is often seen rather as an algorithm than an estimator related to a certain objective function, and only recently has its… (More)

that, under general assumptions, any two scatter matrices with the so called independent components property can be used to estimate the unmixing matrix for the independent component analysis (ICA). The method is a generalization of Cardoso's (Cardoso, 1989) FOBI estimate which uses the regular covariance matrix and a scatter matrix based on fourth moments.… (More)

Deflation-based FastICA is a popular method for independent component analysis. In the standard deflation-based approach the row vectors of the unmixing matrix are extracted one after another always using the same nonlinearities. In practice the user has to choose the nonlinearities and the efficiency and robustness of the estimation procedure then strongly… (More)

For assessing the separation performance (quality and accuracy) of ICA estimators, several performance indices have been introduced in the literature. The purpose of this note is to outline, review and study the properties of performance indices as well as propose some new ones. Special emphasis is put on the properties that such performance indices ought… (More)

In independent subspace analysis (ISA) one assumes that the components of the observed random vector are linear combinations of the components of a latent random vector with independent subvectors. The problem is then to find an estimate of a transformation matrix to recover the independent subvectors. Regular independent component analysis (ICA) is a… (More)

The so-called independent component (IC) model states that the observed p-vector X is generated via X = ΛZ + µ, where µ is a p-vector, Λ is a full-rank matrix, and the centered random vector Z has independent marginals. We consider the problem of testing the null hypothesis H 0 : µ = µ 0 , where µ 0 is a fixed p-vector, on the basis of i.i.d. observations X… (More)