R: Scatter Matrix based on Fourth Moments

cov4 {ICS} | R Documentation

## Scatter Matrix based on Fourth Moments

### Description

Estimates the scatter matrix based on the 4th moments of the data.

### Usage

    cov4(X, location = "Mean", na.action = na.fail)

### Arguments

`X` | numeric data matrix or dataframe, missing values are not allowed.
`location` | can be either `Mean`, `Origin` or numeric. If numeric the matrix is computed wrt to the given location.
`na.action` | a function which indicates what should happen when the data contain 'NA's. Default is to fail.

### Details

If location is `Mean` the scatter matrix of 4th moments is computed wrt to the sample mean. For location = `Origin` it is the scatter matrix of 4th moments wrt to the origin. The scatter matrix is standardized in such a way to be consistent for the regular covariance matrix at the multinormal model. It is given for n x p matrix X by

1/(p+2) ave{[(x_i-x_bar)S^{-1}(x_i-x_bar)'] (x_i-x_bar)'(x_i-x_bar)},

where x_bar is the mean vector and S the regular covariance matrix.

### Value

A matrix.

### Author(s)

Klaus Nordhausen

### References

Cardoso, J.F. (1989), Source separation using higher order moments, in Proc. IEEE Conf. on Acoustics, Speech and Signal Processing (ICASSP'89), 2109–2112. <doi:10.1109/ICASSP.1989.266878>.

Oja, H., Sirkiä, S. and Eriksson, J. (2006), Scatter matrices and independent component analysis, Austrian Journal of Statistics, 35, 175–189.

### Examples

    set.seed(654321)
    cov.matrix <- matrix(c(3,2,1,2,4,-0.5,1,-0.5,2), ncol=3)
    X <- rmvnorm(100, c(0,0,0), cov.matrix)
    cov4(X)
    cov4(X, location="Origin")
    rm(.Random.seed)

[Package ICS version 1.3-0 Index]