臺灣博碩士論文加值系統

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 The perturbation theory provides a useful tool insensitivity analysis for linear discriminant analysis (LDA).Although some influence functions with single-perturbationand local influence in LDA have been discussed,we propose another influence function inspired by Critchley(1985), called the deleted empirical influence functionas an alternative approach to the influence analysis for LDA.It is well-known that single-perturbation diagnosticscan suffer from the masking effect. Hence in this thesis we develop the pair-perturbation influence functions to detect the maskedinfluential points and outliers. An example is providedto illustrate these approaches.
 ContentsAbstract 11 Introduction 12 Pair-Perturbation Influence Functions 22.1 Linear Discriminant Analysis (LDA) . . . . . . . . . . . . . . . . ..32.2 Empirical Influence Functions . . . . . . . . . . . . . . . . . . . 42.3 Deleted Empirical Influence Functions . . . . . . . . . . . . . . . 82.4 Sample Influence Functions . . . . . . . . . . . . . . . . . . . . . 93 Local Influence Functions 114 Cut Points Selection 145 Example 166 Conclusions and Discussion 20References 27Appendix 29
 References[1] Campbell, N. A. (1978), The influence function as an aid in outlier detectionin discriminant analysis, Applied Statistics, 27, 251-258.[2] Cook, R. D. (1986), Assessment of local influence, Journal of the Royal StatisticalSociety, 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 estimationand outlier detection with correlation coefficients, Biometrika, 62, 531-545.[5] Fung,W. K. (1992), Some diagnostic measures in discriminant analysis, Statisticsand Probability Letters, 13, 279-285.[6] Fung, W. K. (1996), The influence of an observation on the misclassificationprobability 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 ofthe American Statistical Association, 69, 383-393.[8] Johnson, R. A. and Wichern, D.W. (2002), Applied Multivariate StatisticalAnalysis, 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 localinfluence, 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 andGraphical Statistics, 10(3), 513-544.[12] Rencher, A. C. (1995), Methods of multivariate analysis, New York: JohnWiley.[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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