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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:120

Article

Kirschstein, Thomas¹  Liebscher, Steffen¹  Becker, Claudia¹ 

[1] Univ Halle Wittenberg, D-06099 Halle, Germany

关键词: Minimum covariance determinant;    Minimum spanning tree;    Outlier identification;    Robust estimation;   

DOI  :  10.1016/j.jmva.2013.05.004

来源: Elsevier

【 摘 要 】

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 nonconvex 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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free