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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Institution: | 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<p;p:number of variables) to investigate the influence onthe subspace spanned by principal components. These influence functions are applicable not only to the case where the edigenvalues of interst are all simple but also to the case where there are some multiple eigenvalues among those of interest. |
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Keywords: | Sensitivity analysis influence functiuon principal component analysis perturbation theory vof eigenvalue problems multiple eigenvalues |
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