cov4 | R Documentation |

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

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

`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. |

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 \times p`

matrix X by

`\frac{1}{p+2} ave_{i}\{[(x_{i}-\bar{x})S^{-1}(x_{i}-\bar{x})'](x_{i}-\bar{x})'(x_{i}-\bar{x})\},`

where `\bar{x}`

is the mean vector and `S`

the regular covariance matrix.

A matrix containing the estimated fourth moments scatter.

Klaus Nordhausen

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., Sirki?, S. and Eriksson, J. (2006), Scatter matrices and independent component analysis, *Austrian Journal of Statistics*, **35**, 175–189.

```
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)
```

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