{
  "creator": [
    "Bénasséni, Jacques",
    "Mom, Alain"
  ],
  "date": [
    "2025-03-31"
  ],
  "description": [
    "Principal component analysis is a well known method for dimension reduction based on the covariance matrix associated to a multivariate data table. Therefore, a large amount of work has been devoted to analyzing the sensitivity of the eigenstructure of this matrix to influential observations. In order to evaluate the effect of deleting one or a small subset of observations, several approximations for the perturbed eigenelements have been proposed. This paper provides a theoretical and numerical comparison of the main approximations. A special emphasis is given to those based on Rayleigh quotients since they are under-utilized given their excellent performance. A general approach, using refined inequalities, is proposed in order to get a precise evaluation of their accuracy without having to recompute the exact perturbed eigenvalues and eigenvectors. This approach is of specific interest from a computational standpoint. Theoretical developments are illustrated with a numerical study which emphasizes the accuracy of approximations based on Rayleigh quotients."
  ],
  "format": [
    "application/pdf",
    "text/html",
    "text/xml"
  ],
  "identifier": [
    "https://meth.psychopen.eu/index.php/meth/article/view/15357",
    "10.5964/meth.15357"
  ],
  "language": [
    "eng"
  ],
  "publisher": [
    "PsychOpen GOLD / Leibniz Institut for Psychology (ZPID)"
  ],
  "relation": [
    "https://meth.psychopen.eu/index.php/meth/article/view/15357/15357.pdf",
    "https://meth.psychopen.eu/index.php/meth/article/view/15357/15357.html",
    "https://meth.psychopen.eu/index.php/meth/article/view/15357/15357.xml"
  ],
  "rights": [
    "Copyright (c) 2025 Jacques Bénasséni, Alain Mom",
    "https://creativecommons.org/licenses/by/4.0"
  ],
  "source": [
    "Methodology; Vol. 21 No. 1 (2025); 27-45",
    "1614-2241",
    "1614-1881",
    "10.5964/meth.v21i1"
  ],
  "subject": [
    "approximation",
    "eigenvalue and eigenvector",
    "covariance matrix",
    "principal component analysis",
    "perturbation",
    "Rayleigh quotient."
  ],
  "title": [
    "A Comparative Study of Approximations for Perturbation Analysis of Principal Components"
  ],
  "type": [
    "info:eu-repo/semantics/article",
    "info:eu-repo/semantics/publishedVersion",
    "Peer-reviewed article"
  ]
}