# 臺灣博碩士論文加值系統

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 The perturbation theory of eigenvalue problems provides a useful mathematical tool in sensitive analysis for Principal Component Analysis ( PCA ). Single-perturbation on influence functions and local influence in PCA has been discussed by many authors. However, it is well known that single-perturbation diagnostics can suffer from a form of masking. Thus, pair-perturbations on influence functions for eigenvalues and eigenvectors need to be developed to detect the masked influential points in PCA. In this thesis, we derive the influence functions and local influence ofpair-perturbations,and examine relationships and make comparisonsamong these influence functions and local influence. An example to these approaches to illustrate the results is also provided.
 Abstract1 Introduction................................................12 Pair-Perturbations on Influence Functions...................2 2.1 Empirical Influence Function............................4 2.2 Deleted Empirical Influence Function....................5 2.3 Sample Influence Function...............................63 Local Influence Function....................................74 Example.....................................................105 Conclusion and Discussion...................................15References....................................................20Appendix......................................................20
 1 Critchley, F.(1985). Influence in principal component analysis. Biometrika 72, 627-636.2 Cook, R. D.(1986). Assessment of local influence. J. R. Statist. Soc. B 48, 133-169.3 Cook, R. D. & Weisberg, S.(1982). Residuals and influence in Regression. New York: Chapman & Hall.4 Dunteman, G. H.(1989). Principal Components Analysis.Sage University Paper.5 Jolliffe, I. T.(1986). Principal Component Analysis. Springer-Verlag.6 Johnson, R. A. & Wichern, D. W.(1998). Applied Multivariate Statistical Analysis, fourth ed. Prentice-Hall.7 Kendall, M. G.(1975). Multivariate Analysis. London: Griffin.8 Shi, L.(1997). Local influence in principal component analysis.Biometrika 84, 175-186.9 Tanaka, Y.(1988). Sensitivity analysis in principal component analysis: influence on the subspace spanned by principal components. Commun. Statist. A 17, 3157-3175.10 Tanaka, Y. & Zhang, F.(1999). R-mode and Q-mode influence analyses in statistical modelling: relationship between influence function approach and local influence approach. Computational Statistics and Data Analysis 32, 197-218.
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