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Efficiency of the pMST and RDELA location and scatter estimators

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  • Steffen Liebscher
  • Thomas Kirschstein

Abstract

The paper proposes two approaches to increase the efficiency of the pMST location and scatter estimator and of the RDELA location and scatter estimator. One approach is deduced from classical reweighting, commonly employed by established robust location and scatter estimators, and the other one is derived from Chebychev’s inequality. Simulation results suggest that both approaches are applicable to increase the efficiency of both estimators. Thereby the classical reweighting approach is outperformed by the approach based on Chebychev’s inequality. Using the latter, the performance of the pMST and RDELA estimator can be brought up to the level of the reweighted minimum covariance determinant and reweighted S-estimator. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:99:y:2015:i:1:p:63-82
    DOI: 10.1007/s10182-014-0231-7
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    References listed on IDEAS

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    1. Joe, Harry, 2006. "Generating random correlation matrices based on partial correlations," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2177-2189, November.
    2. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    3. 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.
    4. Todorov, Valentin & Filzmoser, Peter, 2009. "An Object-Oriented Framework for Robust Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i03).
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    Cited by:

    1. Kirschstein, T. & Liebscher, S. & Porzio, G.C. & Ragozini, G., 2016. "Minimum volume peeling: A robust nonparametric estimator of the multivariate mode," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 456-468.
    2. T. Kirschstein & Steffen Liebscher, 2019. "Assessing the market values of soccer players – a robust analysis of data from German 1. and 2. Bundesliga," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(7), pages 1336-1349, May.

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