臺灣博碩士論文加值系統

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 of
pair-perturbations,and examine relationships and make comparisons
among these influence functions and local influence. An example to these approaches to illustrate the results is also provided.

Abstract
1 Introduction................................................1
2 Pair-Perturbations on Influence Functions...................2
2.1 Empirical Influence Function............................4
2.2 Deleted Empirical Influence Function....................5
2.3 Sample Influence Function...............................6
3 Local Influence Function....................................7
4 Example.....................................................10
5 Conclusion and Discussion...................................15
References....................................................20
Appendix......................................................20

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