A Deterministic Algorithm for Robust Location and Scatter

Most algorithms for highly robust estimators of multivariate location and scatter start by drawing a large number of random subsets. For instance, the FASTMCD algorithm of Rousseeuw and Van Driessen starts in this way, and then takes so-called concentration steps to obtain a more accurate approximat...

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Veröffentlicht in:Journal of computational and graphical statistics Jg. 21; H. 3; S. 618 - 637
Hauptverfasser: Hubert, Mia, Rousseeuw, Peter J., Verdonck, Tim
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Alexandria Taylor & Francis Group 01.09.2012
American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America
Taylor & Francis Ltd
Schlagworte:
Affine equivariance
Algorithms
Analytical estimating
Approximation
Covariance
Covariance matrices
Datasets
Determinism
Estimating techniques
Estimation methods
Estimators
Handling Massive and Complex Data
Multivariate
Optimization algorithms
Outliers
Preliminary estimates
Principal components analysis
Robustness
Studies
ISSN:1061-8600, 1537-2715
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Zusammenfassung:Most algorithms for highly robust estimators of multivariate location and scatter start by drawing a large number of random subsets. For instance, the FASTMCD algorithm of Rousseeuw and Van Driessen starts in this way, and then takes so-called concentration steps to obtain a more accurate approximation to the MCD. The FASTMCD algorithm is affine equivariant but not permutation invariant. In this article, we present a deterministic algorithm, denoted as DetMCD, which does not use random subsets and is even faster. It computes a small number of deterministic initial estimators, followed by concentration steps. DetMCD is permutation invariant and very close to affine equivariant. We compare it to FASTMCD and to the OGK estimator of Maronna and Zamar. We also illustrate it on real and simulated datasets, with applications involving principal component analysis, classification, and time series analysis. Supplemental material (Matlab code of the DetMCD algorithm and the datasets) is available online.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2012.672100