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

The functions below are only for comparison purposes and are all written in R. Each function corresponds to a different algorithm for the scatter only problem for M-estimation using weights coming from the multivariate t-distribution.

1 2 3 4 5 | ```
MVTMLE0r(X, nu = 0, delta = 1e-06, prewhitened = FALSE, steps = FALSE)
MVTMLE0r_FP(X, nu = 0, delta = 1e-06, steps = FALSE)
MVTMLE0r_FP0(X, nu = 0, delta = 1e-06, steps = FALSE)
MVTMLE0r_G(X, nu = 0, delta = 1e-06, steps = FALSE)
MVTMLE0r_CG(X, nu = 0, delta = 1e-06, steps = FALSE)
``` |

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

`nu` |
assumed degrees of freedom of the t-distribution. Must be 0 or larger. Default is '0' which corresponds to Tyler's shape matrix. |

`delta` |
convergence tolerance, which means that the algorithms stop when the Frobenius norm of the gradient is smaller than delta. |

`prewhitened` |
logical. Is the data prewhitened or not. |

`steps` |
logial. If TRUE intermediate results are printed on the console. |

All functions are implemented in R and their purpose is only for demonstration of the differences of the different algorithms.
The function `MVTMLE0r`

uses the recommended partial Newton approach as implemented also in (`MVTMLE`

and `TYLERshape`

).
`MVTMLE0r_FP`

and `MVTMLE0r_FP0`

are fixed-point algorithms where `MVTMLE0r_FP`

iterates the fixed point equation with
'iterative whitening' of the data. The function `MVTMLE0r_G`

uses a gradient approach and `MVTMLE0r_CG`

a conjugate gradient approach.
Note that `MVTMLE0r_CG`

does not check if the 'next' step is really an improvement and that all functions compute the scatter wrt to the origin.

All functions have a hard coded maximum number of iterations of 1000. If that is reached the functions returns the final estimate, however without a warning.

For general purposes we recommend the functions `MVTMLE`

and `TYLERshape`

.

A list containing at least:

`S` |
Estimated scatter matrix (or shape matrix if |

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

Lutz Duembgen and Klaus Nordhausen

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

1 2 3 4 5 | ```
MVTMLE0r(longley,nu=1)
MVTMLE0r_FP(longley,nu=1)
MVTMLE0r_FP0(longley,nu=1)
MVTMLE0r_G(longley,nu=1)
MVTMLE0r_CG(longley,nu=1)
``` |

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