Effects of observations on the eigensystem of a sample covariance matrix

DOI10.1016/0378-3758(93)90125-PzbMath0778.62053OpenAlexW2022605463MaRDI QIDQ689389

Erkki P. Liski, Song-Gui Wang

Publication date: 2 December 1993

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-3758(93)90125-p

zbMATH Keywords

eigenvectorspower series expansionsdeleting observationsdetection of influential observationsmatrix perturbation analysisperturbed sample covariance matrixprincipal component valuesunrepeated eigenvalues

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Estimation in multivariate analysis (62H12) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items

Inequalities for the eigenvectors associated to extremal eigenvalues in rank one perturbations of symmetric matrices, A concentration approach to sensitivity studies in statistical estimation problems, A correction of approximations used in sensitivity study of principal component analysis, On the algebraic relation between principal components corresponding to two different sets of weights, A concentration study of principal components

Cites Work

• 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 Function as an Aid in Outlier Detection in Discriminant Analysis
• Quadratic perturbation expansions of certain functions of eigenvalues and eigenvectors and their application to sensitivity analysis in multivariate methods
• Influence functions for certain parameters in multivariate analysis
• Robust Statistics
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