Quadratic perturbation expansions of certain functions of eigenvalues and eigenvectors and their application to sensitivity analysis in multivariate methods

DOI10.1080/03610929008830358zbMath0736.62051OpenAlexW2129368216MaRDI QIDQ3978088

Eduardo Castaño-Tostado, Yutaka Tanaka

Publication date: 25 June 1992

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610929008830358

zbMATH Keywords

sensitivity analysisprincipal component analysisperturbation expansionsinfluence functionsinfluential observationquadratic termsperturbation theory of eigenvalue problemsprincipal factor analysis

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (6)

A note on sensitivity of principal component subspaces and the efficient detection of influential observations in high dimensions ⋮ Using conditional bias in principal component analysis for the evaluation of joint influence on the eigenvalues of the covariance matrix ⋮ A new and practical influence measure for subsets of covariance matrix sample principal components with applications to high dimensional datasets ⋮ Influence Analysis in Principal Component Analysis Through Power-Series Expansions ⋮ Effects of observations on the eigensystem of a sample covariance matrix ⋮ Sensitivity of principal component subspaces: a comment on Prendergast's paper

Cites Work

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• Methods of matrix algebra
• Sensitivity analysis in maximum likelihood factor analysis
• Influence functions related to eigenvalue problems which appear in multivariate analysis
• Sensitivity analysis in principal component analysis:influence on the subspace spanned by principal components.
• Influence in principal components analysis
• The Influence Curve and Its Role in Robust Estimation
• Influence functions for certain parameters in multivariate analysis

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