Principal component analysis based on robust estimators of the covariance or correlation matrix: Influence functions and efficiencies

• 成果类型: Article
• 署名作者: Croux, C; Haesbroeck, G
• 署名单位: Universite Libre de Bruxelles; University of Liege
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/87.3.603
• 发表日期: 2000
• 页码: 603618
• 关键词: multivariate location; dispersion matrices

摘要

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.