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

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  • Kirschstein, Thomas
  • Liebscher, Steffen
  • Becker, Claudia

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.

Suggested Citation

  • Kirschstein, Thomas & Liebscher, Steffen & Becker, Claudia, 2013. "Robust estimation of location and scatter by pruning the minimum spanning tree," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 173-184.
    • Handle: RePEc:eee:jmvana:v:120:y:2013:i:c:p:173-184
    DOI: 10.1016/j.jmva.2013.05.004
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    References listed on IDEAS

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    3. Caroni, C. & Prescott, P., 1995. "On Rohlf's Method for the Detection of Outliers in Multivariate Data," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 295-307, February.
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    Cited by:

    1. Kirschstein, Thomas & Liebscher, Steffen & Pandolfo, Giuseppe & Porzio, Giovanni C. & Ragozini, Giancarlo, 2019. "On finite-sample robustness of directional location estimators," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 53-75.
    2. Mathias Kloss & Thomas Kirschstein & Steffen Liebscher & Martin Petrick, 2019. "Robust Productivity Analysis: An application to German FADN data," Papers 1902.00678, arXiv.org, revised Feb 2019.
    3. Steffen Liebscher & Thomas Kirschstein, 2015. "Efficiency of the pMST and RDELA location and scatter estimators," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 63-82, January.

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