Principal component analysis based on robust estimators of the covariance or correlation matrix: Influence functions and efficiencies. (English) Zbl 0956.62047

Croux, Christophe; Haesbroeck, Gentiane

Biometrika 87, No. 3, 603-618 (2000).

Summary: 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. 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.

MSC:

62H25	Factor analysis and principal components; correspondence analysis
62F35	Robustness and adaptive procedures (parametric inference)

Keywords:

robust correlation matrix; principal component analysis; influence functions; robust estimators