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JADE solves the blind source separation problem in the case of independent components with at most one component having kurtosis values zero, while FOBI requires distinct kurtosis values. The functions compute the asymptotic covariance matrices of JADE and FOBI estimates for the mixing or the unmixing matrix.
ASCOV_JADE_est(X, mixed=TRUE)ASCOV_FOBI_est(X, mixed=TRUE)
A list with the following components:
estimated mean of the unmixing matrix estimate.
estimated covariance matrix of the unmixing matrix estimate.
estimated mean of the mixing matrix estimate.
estimated covariance matrix of the mixing matrix estimate.
a numeric data matrixx.
logical, see details.
Jari Miettinen
If mixed is TRUE, then X will be transformed by the corresponding estimate. The option FALSE can be used, for example, to estimate the covariance when X are source estimates given by some other method than JADE or FOBI.
Ilmonen, P., Nevalainen, J. and Oja, H. (2010), Characteristics of multivariate distributions and the invariant coordinate system, Statistics and Probability Letters, 80, 1844--1853.
Miettinen, J., Taskinen S., Nordhausen, K. and Oja, H. (2015), Fourth Moments and Independent Component Analysis, Statistical Science, 30, 372--390.
ASCOV_JADE, ASCOV_FOBI, JADE, FOBI
# source components have t-10-, uniform- and gaussian distribution
s1 <- rt(1000,10)/sqrt(10/8)
s2 <- runif(1000,-sqrt(3),sqrt(3))
s3 <- rnorm(1000)
S <- cbind(s1,s2,s3)
A <- matrix(rnorm(9),3,3)
X <- S %*% t(A)
round(1000*ASCOV_JADE_est(X)$COV_W,2)
round(1000*ASCOV_FOBI_est(X)$COV_W,2)
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