Search

Despite of the increased interest in independent component analysis (ICA) during the past two decades, a simple closed form expression of the Cramér-Rao bound (CRB) for the demixing matrix estimation has not been established in the open literature. In the present paper we fill this gap by deriving a simple closed-form expression for the CRB of the demixing matrix directly from its definition. A simulation study comparing ICA estimators with the CRB is given. [ABSTRACT FROM AUTHOR]

We introduce a new equivariant estimation method of the parameters of the multivariate regression model with q responses and p regressors. The estimate matrix is derived from the lift rank covariance matrix (LRCM) where the lift rank vectors are based on the Oja criterion function. The k = p + q variate ranks and k + 1 variate lift ranks are constructed using hyperplanes (or fits) going through k observations. The new LRCM regression estimate and the least squares (LS) estimate are shown to be weighted sums of the elemental estimates based on these hyperplanes. The LRCM regression estimate is equivariant and convergent, has a limiting multinormal distribution, and is highly efficient in the multivariate normal case. For heavy-tailed distributions, it performs better than the standard LS estimate. Estimation of the variance-covariance matrix of the LRCM estimate is briefly discussed. The theory is illustrated by simulations and a real data example. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler''s shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example. [Copyright &y& Elsevier]