Robustifying principal component analysis with spatial sign vectors

DOI10.1016/j.spl.2012.01.001zbMath1243.62084OpenAlexW2150136439WikidataQ109744820 ScholiaQ109744820MaRDI QIDQ434715

Inge Koch, Sara Taskinen, Hannu Oja

Publication date: 16 July 2012

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: http://urn.fi/URN:NBN:fi:jyu-201211293124

zbMATH Keywords

robustnessefficiencyinfluence functionaffine equivariancespatial sign vector

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Factor analysis and principal components; correspondence analysis (62H25) Estimation in multivariate analysis (62H12) Robustness and adaptive procedures (parametric inference) (62F35)

Related Items

On the eigenvalues of the spatial sign covariance matrix in more than two dimensions, On weighted multivariate sign functions, A generalized spatial sign covariance matrix, Robust Functional Principal Component Analysis via a Functional Pairwise Spatial Sign Operator, Gini covariance matrix and its affine equivariant version, Sign tests for weak principal directions, Robustifying multiple-set linear canonical analysis with S-estimator, Fast estimation of the median covariation matrix with application to online robust principal components analysis, ECA: High-Dimensional Elliptical Component Analysis in Non-Gaussian Distributions, Efficient R-Estimation of Principal and Common Principal Components, On the eigenvectors of large-dimensional sample spatial sign covariance matrices

Uses Software

• MNM

Cites Work

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• A canonical definition of shape
• Multivariate nonparametric methods with R. An approach based on spatial signs and ranks.
• A note on multivariate location and scatter statistics for sparse data sets
• Asymptotic distributions of robust shape matrices and scales
• A distribution-free M-estimator of multivariate scatter
• On Tyler's \(M\)-functional of scatter in high dimension
• Robust principal component analysis for functional data. (With comments)
• Some robust estimates of principal components
• Symmetrised M-estimators of multivariate scatter
• Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices
• Multivariate nonparametric tests
• Robust functional estimation using the median and spherical principal components
• Sensitivity analysis in principal component analysis:influence on the subspace spanned by principal components.
• Robust Estimation of Dispersion Matrices and Principal Components
• A practical affine equivariant multivariate median
• Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies
• On the Breakdown Properties of Some Multivariate M-Functionals*
• Asymptotic Theory for Principal Component Analysis
• Sign and rank covariance matrices
• A modified Weiszfeld algorithm for the Fermat-Weber location problem