Tanaka, Yutaka; Zhang, Fanghong; Mori, Yuichi Local influence in principal component analysis: relationship between the local influence and influence function approaches revisited. (English) Zbl 1430.62124 Comput. Stat. Data Anal. 44, No. 1-2, 143-160 (2003). Summary: Influence analysis is developed on the basis of Cook’s local influence in its original form, i.e., using the likelihood displacement as the criterion function for studying jointly as well as singly influential observations in principal component analysis (PCA). It is found that the derived influential directions are equivalent to the standardized vectors of the principal component scores obtained by PCA with metric \(V^{ - }\) of the influence functions of PCA parameters \(\hat{\theta}\), where \(V\) is a consistent estimate for the asymptotic covariance matrix of \(\hat{\theta}\) and superscript \((^{ - })\) indicates a g-inverse. 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