Robust estimation of location and scatter by pruning the minimum spanning tree

Thomas Kirschstein, Steffen Liebscher and Claudia Becker

Journal of Multivariate Analysis, 2013, vol. 120, issue C, 173-184

Abstract: One of the most essential topics in robust statistics is the robust estimation of location and covariance. Many popular robust (location and scatter) estimators such as Fast-MCD, MVE, and MZE require at least a convex distribution of the underlying data. In the case of non-convex data distributions these approaches may lead to a suboptimal result caused by the application of Mahalanobis distances with respect to location and covariance of a suitably chosen subsample of the data—implying a convex structure. The approach presented here fixes this drawback using Euclidean distances. The data set is treated as a complete network and the minimum spanning tree (MST) for this data set is calculated. Based on the MST a subset of relevant points (thought of as an “outlier-free” subsample of minimum size) is determined which can then be used for calculating data characteristics. It is shown, that the approach has a maximum breakdown point. Additionally, a simulation study provides insights in the approach’s behaviour with respect to increasing dimension and size.

Keywords: Minimum covariance determinant; Minimum spanning tree; Outlier identification; Robust estimation (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.jmva.2013.05.004

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