Sensitivity analysis in principal component analysis:influence on the subspace spanned by principal components. |
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| Authors: | Yukata Tanaka |
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| Affiliation: | Department of Statistics , Okayama university , Tsushima , okayama , 700 , Japan |
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| Abstract: | The problem of detecting influential observations in principalcomponent analysis was discussed by several authors. Radhakrishnan and kshirsagar ( 1981 ), Critchley ( 1985 ), jolliffe ( 1986 )among others discussed this topicby using the influence functions I(X;θs)and I(X;Vs)of eigenvalues and eigenvectors, which wwere derived under the assumption that the eigenvalues of interest were simple. In this paper we propose the influence functionsI(X;∑q s=1θsVsVs T)and I(x;∑q s=1VsVs t)(q
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| Keywords: | Sensitivity analysis influence functiuon principal component analysis perturbation theory vof eigenvalue problems multiple eigenvalues |
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