ASCOV_JADE_est {BSSasymp}

Asymptotic covariance matrix of JADE and FOBI estimates

Description

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.

Usage

ASCOV_JADE_est(X, mixed=TRUE)

ASCOV_FOBI_est(X, mixed=TRUE)

Arguments

X

a numeric data matrixx.

mixed

logical, see details.

Details

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.

Value

A list with the following components:

W

estimated mean of the unmixing matrix estimate.

COV_W

estimated covariance matrix of the unmixing matrix estimate.

A

estimated mean of the mixing matrix estimate.

COV_A

estimated covariance matrix of the mixing matrix estimate.

Author(s)

Jari Miettinen

References

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.

See Also

ASCOV_JADE, ASCOV_FOBI, JADE, FOBI

Examples

# 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)