# The RDELA Algorithm

### Description

The function determines a robust subsample utilizing the Delaunay triangulation.

### Usage

1 |

### Arguments

`data` |
At least a two-dimensional data matrix is required. Number of observations needs to be greater than the number of dimensions. No degenerated (i.e. collinear) data sets allowed. |

`N` |
Size of the identified subsample. Default is |

`rew` |
Logical. Specifies whether reweighting should be conducted (TRUE) or not (FALSE). Default is TRUE. |

### Details

The function first calls the `delaunayn`

function within the geometry-package. The results are subsequently used to determine a robust subsample.

### Value

`data` |
The input data set. |

`tri` |
Vertices of all simplices of the Delaunay triangulation. Each row represents a simplex. |

`neigh` |
Lists for every simplex the adjacent/neighboring simplices. Each list entry represents a simplex. |

`radii` |
Circum-(hypersphere-)radius of each simplex. |

`center` |
Center coordinates of all simplices. |

`LiB` |
List of all basins found. Index of simplices. Smallest subsample of size |

`LiN` |
List of all neighboring simplices per basin. Index of simplices. Smallest subsample of size |

`GeB` |
Number of associated data points per basin. Smallest subsample of size |

`drin` |
(Initial) Robust subsample of size N. |

`raw.mean` |
Mean estimate based on (initial) robust subsample of size N. |

`raw.cov` |
Covariance estimate based on (initial) robust subsample of size N. |

`final` |
Final robust subsample after reweighting. |

`mean` |
Mean estimate based on final robust subsample. |

`cov` |
Covariance estimate based on final robust subsample. |

### Author(s)

Steffen Liebscher <steffen.liebscher@wiwi.uni-halle.de>

### References

Liebscher, S., Kirschstein, T. (2015): Efficiency of the pMST and RDELA Location and Scatter Estimators, *AStA-Advances in Statistical Analysis*, 99(1), 63-82, DOI: 10.1007/s10182-014-0231-7.

Liebscher, S., Kirschstein, T., and Becker, C. (2013): RDELA - A Delaunay-Triangulation-based, Location and Covariance Estimator with High Breakdown Point, *Statistics and Computing*, DOI: 10.1007/s11222-012-9337-5.

### Examples

1 | ```
# rdela(halle)
``` |