Description Usage Arguments Details Value Author(s) References See Also Examples

The algorithm of this function is based on a partial Newton approach and should be faster than the traditional fixed-point algorithm. If the data follows a multivariate t-distribution with the correctly specified degrees of freedom this function gives the maximum likelihood estimate of location and scatter.

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

`nu` |
assumed degrees of freedom of the t-distribution. Default is '1' which corresponds to the Cauchy distribution. |

`location` |
logical or numeric. If FALSE, it is assumed that the scatter should be computed wrt to the origin. If TRUE the location will be estimated and if it is a numeric vector it will be computed wrt to this vector. |

`eps` |
convergence tolerance, which means that the algorithm stops when the Frobenius norm of the gradient is smaller than eps. |

`maxiter` |
maximum number of iterations. |

The assumed degree of freedom nu must be at least 1 when the location and scatter should be estimated. If only the scatter is to be estimated, then it needs to be larger than zero only.

In case `maxiter`

is reached before convergence, the estimate at that iteration is returned and a warning is given.

A list containing:

`mu` |
Estimated location if |

`Sigma` |
Estimated scatter matrix. |

`iter` |
Number of iterations of the algorithm. |

Lutz Duembgen and Klaus Nordhausen

Kent, J.T., Tyler, D.E. and Vardi, Y. (1994), A curious likelihood identity for the multivariate t-distribution, *Communications in Statistics, Theory and Methods*, **23**, 441–453.

Duembgen, L., Nordhausen, K. and Schuhmacher, H. (2016), New algorithms for M-estimation of multivariate location and scatter, *Journal of Multivariate Analysis*, **144**, 200–217. doi: 10.1016/j.jmva.2015.11.009

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