The RDELA Algorithm

Description

The function determines a robust subsample utilizing the Delaunay triangulation.

Usage

1
rdela(data, N, rew=TRUE)

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 (n+d+1)/2.

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 (n+d+1)/2.

LiN

List of all neighboring simplices per basin. Index of simplices. Smallest subsample of size (n+d+1)/2.

GeB

Number of associated data points per basin. Smallest subsample of size (n+d+1)/2.

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)