RDELA--a Delaunay-triangulation-based, location and covariance estimator with high breakdown point

Authors:
Steffen Liebscher;Thomas Kirschstein;Claudia Becker
Affiliations:
Martin-Luther-University, Halle (Saale), Germany 06099;Martin-Luther-University, Halle (Saale), Germany 06099;Martin-Luther-University, Halle (Saale), Germany 06099
Venue:
Statistics and Computing
Year:
2013

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Abstract

We propose an approach that utilizes the Delaunay triangulation to identify a robust/outlier-free subsample. Given that the data structure of the non-outlying points is convex (e.g. of elliptical shape), this subsample can then be used to give a robust estimation of location and scatter (by applying the classical mean and covariance). The estimators derived from our approach are shown to have a high breakdown point. In addition, we provide a diagnostic plot to expand the initial subset in a data-driven way, further increasing the estimators' efficiency.