Description Usage Arguments Value Author(s) References Examples

Calculates the moments of the sample covariance matrix. It assumes that the summands (the outer products of the samples' random data vector) that constitute the sample covariance matrix follow a Wishart-distribution with scale parameter *\mathbf{Σ}* and shape parameter *ν*. The latter is equal to the number of summands in the sample covariance estimate.

1 | ```
momentS(Sigma, shape, moment=1)
``` |

`Sigma` |
Positive-definite |

`shape` |
A |

`moment` |
An |

The *r*-th moment of a sample covariance matrix: *E(\mathbf{S}^r)*.

Wessel N. van Wieringen.

Lesac, G., Massam, H. (2004), "All invariant moments of the Wishart distribution", *Scandinavian Journal of Statistics*, 31(2), 295-318.

1 2 3 4 5 6 7 | ```
# create scale parameter
Sigma <- matrix(c(1, 0.5, 0, 0.5, 1, 0, 0, 0, 1), byrow=TRUE, ncol=3)
# evaluate expectation of the square of a sample covariance matrix
# that is assumed to Wishart-distributed random variable with the
# above scale parameter Sigma and shape parameter equal to 40.
momentS(Sigma, 40, 2)
``` |

CFWP/rags2ridges documentation built on Sept. 23, 2017, 6:38 a.m.

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