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Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies
Open accessAbstract
A robust principal component analysis can be easily performed by computing the eigenvalues and eigenvectors of a robust estimator of the covariance or correlation matrix. In this paper we derive the influence functions and the corresponding asymptotic variances for these robust estimators of eigenvalues and eigenvectors. The behaviour of several of these estimators is investigated by a simulation study. It turns out that the theoretical results and simulations favour the use of S-estimators, since they combine a high efficiency with appealing robustness properties.
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Cited by
ROBPCA: A New Approach to Robust Principal Component Analysis
Hubert, M., Rousseeuw, P. J., & Vanden Branden, K. (2005) · Technometrics · doi:10.1198/004017004000000563 · Cited by 1,052
Robust estimation of Cronbach's alpha
Christmann, A., & Van Aelst, S. (2006) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2005.05.012 · Cited by 427
Robust statistics in data analysis — A review
Daszykowski, M., Kaczmarek, K., Vander Heyden, Y., & Walczak, B. (2007) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2006.06.016 · Cited by 331
Zhu, J., Ge, Z., Song, Z., & Gao, F. (2018) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2018.09.003 · Cited by 308
Algorithms for Projection–Pursuit robust principal component analysis
Croux, C., Filzmoser, P., & Oliveira, M. R. (2007) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2007.01.004 · Cited by 285
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Metadata
- Authors
- Croux, C.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 2000-09-01
- Volume
- 87
- Issue
- 3
- Pages
- 603-618
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2055894834
- Cited by
- 370
- References
- 0
- FWCI
- 11.63
- Type
- journal article
- Language
- en
- Open access
- green
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