Jacobi Angles for Simultaneous Diagonalization
SIAM Journal on Matrix Analysis and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Portfolio value at risk based on independent component analysis
Journal of Computational and Applied Mathematics
Handbook of Blind Source Separation: Independent Component Analysis and Applications
Handbook of Blind Source Separation: Independent Component Analysis and Applications
IEEE Transactions on Signal Processing
A new performance index for ICA: properties, computation and asymptotic analysis
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Multivariate versions of Bartlett's formula
Journal of Multivariate Analysis
Joint diagonalization of several scatter matrices for ICA
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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In this paper we assume that the observed p time series are linear combinations of p latent uncorrelated weakly stationary time series. The problem is then to find an estimate for an unmixing matrix that transforms the observed time series back to uncorrelated time series. The so called SOBI (Second Order Blind Identification) estimate aims at a joint diagonalization of the covariance matrix and several autocovariance matrices with varying lags. In this paper, we propose a novel procedure that extracts the latent time series one by one. The limiting distribution of this deflation-based SOBI is found under general conditions, and we show how the results can be used for the comparison of estimates. The exact formula for the limiting covariance matrix of the deflation-based SOBI estimate is given for general multivariate MA(~) processes. Finally, a whole family of estimates is proposed with the deflation-based SOBI as a special case, and the limiting properties of these estimates are found as well. The theory is widely illustrated by simulation studies.