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Using conditional bias in principal component analysis for the evaluation of joint influence on the eigenvalues of the covariance matrix

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
218
Issue
17
Identifiers
DOI: 10.1016/j.amc.2012.02.054
Keywords
  • Conditional Bias
  • Eigenvalue
  • Joint Influence Analysis
  • Principal Component Analysis
Disciplines
  • Medicine

Abstract

Abstract Influence Analysis in Principal Component Analysis has usually been tackled using the influence function [1] or local influence [2] approaches. The main objective of this paper is that of proposing influence diagnostics for the eigenvalues of the covariance matrix, that is, for the variance explained by the principal components, from a different angle: that of the conditional bias [3]. An approximation of the conditional bias of the simple eigenvalues of the sample covariance matrix is calculated under normality and some influence diagnostics are proposed. The study is carried by considering joint influence.

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