# Scatter Matrix based on Fourth Moments

### Description

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

### Usage

1 |

### Arguments

`X` |
numeric data matrix or dataframe, missing values are not allowed. |

`location` |
can be either |

`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

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