The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Minimum volume ellipsoid
Open accessAbstract
The minimum volume ellipsoid (MVE) estimator is based on the smallest volume ellipsoid that covers h of the n observations. It is an affine equivariant, high‐breakdown robust estimator of multivariate location and scatter. The MVE can be computed by a resampling algorithm. Its low bias makes the MVE very useful for outlier detection in multivariate data, often through the use of MVE‐based robust distances. We review the basic MVE definition as well as some useful extensions such as the one‐step reweighted MVE. We discuss the main properties of the MVE including its breakdown value, affine equivariance, and efficiency. We discuss the basic resampling algorithm to calculate the MVE and illustrate its use on two examples. An overview of applications is given, as well as some related classes of robust estimators of multivariate location and scatter. Copyright © 2009 John Wiley & Sons, Inc. This article is categorized under:Statistical and Graphical Methods of Data Analysis > Robust Methods
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Citations
Cites
Robust Regression and Outlier Detection
Rousseeuw, P. J., & Leroy, A. M. (1987) · Wiley Series in Probability and Statistics · doi:10.1002/0471725382 · Cited by 5,609
Self-citationThe identification of multiple outliers
Davies, L., & Gather, U. (1993) · Journal of the American Statistical Association · doi:10.1080/01621459.1993.10476339 · Cited by 709
Breakdown Points of Affine Equivariant Estimators of Multivariate Location and Covariance Matrices
Lopuhaa, H. P., & Rousseeuw, P. J. (1991) · The Annals of Statistics · doi:10.1214/aos/1176347978 · Cited by 446
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Cited by
Osorio‐Olvera, L., Lira‐Noriega, A., Soberón, J., Peterson, A. T., Falconi, M., Contreras‐Díaz, R. G., Martínez‐Meyer, E., Barve, V., & Barve, N. (2020) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.13452 · Cited by 371
Zhu, J., Ge, Z., Song, Z., & Gao, F. (2018) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2018.09.003 · Cited by 308
Metadata
- Authors
- Van Aelst, S., & Rousseeuw, P.
- Venue
- WIREs Computational Statistics
- Publisher
- Wiley
- Published
- 2009-07
- Volume
- 1
- Issue
- 1
- Pages
- 71-82
- ISSN
- 1939-0068 (ISSN-L)
- 1939-5108
- OpenAlex
- W2025970186
- Cited by
- 205
- References
- 3
- FWCI
- 3.28
- Type
- journal article
- Language
- en
- Open access
- green
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