Journal ArticleDOI
Sensitivity coefficients for the subspaces spanned by principal components
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TLDR
In this paper, a different approach based on some measures of closeness between the subspaces spanned by the initial eigenvectors and their corresponding version derived from an infinitesimal perturbation of the data distribution is proposed.Abstract:
In the context of sensitivity analysis in principal component analysis, Tanaka (1988) tackles the problem of the stability of the subspace spanned by dominant principal components. He derives the influence functions related to the projection operator on this subspace and to the spectral decomposition of the covariance or correlation matrix as sensitivity indicators. We suggest here a different approach based on some measures of closeness between the subspaces spanned by the initial eigenvectors and their corresponding version derived from an infinitesimal perturbation of the data distribution.read more
Citations
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Journal ArticleDOI
Factor Analysis and Principal Components
H. Schneeweiss,H. Mathes +1 more
TL;DR: In this paper, the principal components of a vector of random variables are related to the common factors of a factor analysis model for this vector and conditions are presented under which components and factors as well as factor proxies come close to each other.
Journal ArticleDOI
Influence functions for sliced inverse regression.
TL;DR: In this paper, the robustness of SIR is investigated by deriving and plotting the influence function for a variety of contamination structures, and the asymptotic variance of the estimates is also derived for the single index model when the explanatory variable is known to be normally distributed.
Journal ArticleDOI
Implications of influence function analysis for sliced inverse regression and sliced average variance estimation
TL;DR: In this article, the authors compared the sensitivity of sliced inverse regression and sliced average variance estimation to particular observational types and developed an efficient sample version of the influence function to compare the sensitivity.
Journal ArticleDOI
A 50-year personal journey through time with principal component analysis
TL;DR: An account of my 50-year journey through time with PCA would be a suitable topic for inclusion in the Jubilee Issue of JMVA and this is the result.
References
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Book
Principal Component Analysis
TL;DR: In this article, the authors present a graphical representation of data using Principal Component Analysis (PCA) for time series and other non-independent data, as well as a generalization and adaptation of principal component analysis.
Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Journal ArticleDOI
A Unifying Tool for Linear Multivariate Statistical Methods: The RV-Coefficient
P. Robert,Y. Escoufier +1 more
TL;DR: In this article, it is shown that most classical methods of linear multivariate statistical analysis can be interpreted as the search for optimal linear transformations or, equivalently, the searching for optimal metrics to apply on two data matrices on the same sample; the optimality is defined in terms of the similarity of the corresponding configurations of points, which, in turn, calls for the maximization of the associated RV•coefficient.