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研究生:高慈苓
研究生(外文):Tsyrling Kao
論文名稱(外文):Influence Functions and Local Influence in Linear Discriminant Analysis
指導教授:黃郁芬黃郁芬引用關係
指導教授(外文):Yufen Huang
學位類別:碩士
校院名稱:國立中正大學
系所名稱:數理統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:英文
外文關鍵詞:influence functionlocal influencelinear discriminant analysisdiagnostics
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The perturbation theory provides a useful tool in
sensitivity analysis for linear discriminant analysis (LDA).
Although some influence functions with single-perturbation
and local influence in LDA have been discussed,
we propose another influence function inspired by Critchley
(1985), called the deleted empirical influence function
as an alternative approach to the influence analysis for LDA.
It is well-known that single-perturbation diagnostics
can suffer from the masking effect. Hence in this thesis we develop the pair-perturbation influence functions to detect the masked
influential points and outliers. An example is provided
to illustrate these approaches.
Contents
Abstract 1
1 Introduction 1
2 Pair-Perturbation Influence Functions 2
2.1 Linear Discriminant Analysis (LDA) . . . . . . . . . . . . . . . . ..3
2.2 Empirical Influence Functions . . . . . . . . . . . . . . . . . . . 4
2.3 Deleted Empirical Influence Functions . . . . . . . . . . . . . . . 8
2.4 Sample Influence Functions . . . . . . . . . . . . . . . . . . . . . 9
3 Local Influence Functions 11
4 Cut Points Selection 14
5 Example 16
6 Conclusions and Discussion 20
References 27
Appendix 29
References
[1] Campbell, N. A. (1978), The influence function as an aid in outlier detection
in discriminant analysis, Applied Statistics, 27, 251-258.
[2] Cook, R. D. (1986), Assessment of local influence, Journal of the Royal Statistical
Society, B 48, 133-169.
[3] Critchley, F. (1985), Influence in principal component analysis, Biometrika,
72, 627-636.
[4] Devlin, S. J., Gnanadesikan, R. and Kettenring, J. R. (1975), Robust estimation
and outlier detection with correlation coefficients, Biometrika, 62, 531-545.
[5] Fung,W. K. (1992), Some diagnostic measures in discriminant analysis, Statistics
and Probability Letters, 13, 279-285.
[6] Fung, W. K. (1996), The influence of an observation on the misclassification
probability in multiple discriminant analysis, Communications in Statistics-
Theory and Methods, 25, 1917-1930.
[7] Hampel, F. (1974), The influence curve and its role in estimation, Journal of
the American Statistical Association, 69, 383-393.
[8] Johnson, R. A. and Wichern, D.W. (2002), Applied Multivariate Statistical
Analysis, 5th Edition, Prentice-Hall, London.
[9] Johnson, W. (1987), The detection of influential observations for allocation,
separation, and the determination of probabilities in a Bayesian framework,
Journal of Business and Economic Statistics, 5, 369-381.
[10] Lawrance, A. J. (1988), Regression transformation diagnostics using local
influence, Journal of the American Statistical Association, 83, 1067-1072.
[11] Riani, M. and Atkinson, A. C. (2001), A unified approach to outliers, inuence,
and transformations in discriminant analysis, Journal of Computational and
Graphical Statistics, 10(3), 513-544.
[12] Rencher, A. C. (1995), Methods of multivariate analysis, New York: John
Wiley.
[13] Seber, G. A. F. (1984), Multivariate observations, New York: John Wiley.
[14] Szekely, G. J. and Rizzo, M. L. (2005), A New Test for Multivariate Normality,
Journal of Multivariate Analysis, 93(1), 58-80.
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