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https://ah.lib.nccu.edu.tw/handle/140.119/36658| 題名: | Robust Diagnostics for the Logistic Regression Model With Incomplete Data | 作者: | 范少華 | 貢獻者: | 鄭宗記 范少華 |
關鍵詞: | EM algorithm Incomplete data generalized linear model high breakdown ppint robust methods |
日期: | 2002 | 上傳時間: | 18-Sep-2009 | 摘要: | Atkinson 及 Riani 應用前進搜尋演算法來處理百牡利資料中所包含的多重離群值(2001）。在這篇論文中，我們沿用相同的想法來處理在不完整資料下一般線性模型中的多重離群值。這個演算法藉由先填補資料中遺漏的部分，再利用前進搜尋演算法來確認資料中的離群值。我們所提出的方法可以解決處理多重離群值時常會遇到的遮蓋效應。我們應用了一些真實資料來說明這個演算法並得到令人滿意結果。 Atkinson and Riani (2001) apply the forward search algorithm to deal with the problem of the detection of multiple outliers in binomial data.\r\nIn this thesis, we extend the similar idea to identify multiple outliers for the generalized linear models when part of data are missing. The algorithm starts with imputation method to\r\nfill-in the missing observations in the data, and then use the forward search algorithm to confirm outliers. The proposed method can overcome the masking effect, which commonly occurs when multiple outliers exit in the data. Real data are used to illustrate the procedure, and satisfactory results are obtained. |
參考文獻: | Atkinson, A. C. (1994). ”Fast very robust methods for the detection o smultiple outliers”, Hournal of the American Association 89, 1329-1339. Atkinson, A. C. and Riani, M. (2001). ”Regression diagnostics for binomial data from the forward search”, The Statistician, 50, 63-78. Atkinson, A. C. and Riani, M. (2000). Robust Diagnostic Regression Analysis, New York: Springer. Beaton, A. E. (1964). ”The use of special matrix operations in statitical calculus”, Educational Testing Service Research Bulletin, RB, 64-52. Belsey, D. A., Kuh, E., and Welsch, R.E. (1980). Regression Diagnostics: Identifying In?uential Data and Sources of Collinearity, New York: Wiley. Bliss, C. I. (1935). ”The calculation of the dosage-mortality curve”, Annals of Applied Biology 22, 134-167. Christmann, A. (1994). ”Least median of weight squared in logistic regression with large strata”,Biometrika, 81, 413-417. Collett, D., (1991). Modelling Binary Data, London: Chapman & Hall. Cook, R. D., (1977). ”Detection of in?uential observations in linear regression”, Technometrics, 19, 15-18. Cook, R. D., and Weisberg, S., (1982). Residuals and In?uence in Regression, London: Chapman & Hall. Cook, R. D., and Weisberg, S., (1999). Applied Regression Including Computing and Graphics, New York: John Wiley & Sons. Croux, C., Flandre, C. and Haesbroeck,G. (2002). ”The breakdown behavior of the maximum likelihood estimator in the logistic regression”, Statistics & Probability Letters 60, 377- 386. Dempster, A. P. (1969). Elements of Continuous Multivariate Analysis. Addison-Wesley, Reading, MA. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1997). ”Maximum likelihood from incomplete data via the EM algorithm (with discussion)”, J. Roy. Statist. Soc. 39, 1-38. Donoho, D. L., and Huber, P. J. (1983). The Notion of Breakdown Point. In A Festschrift for Erich L. Lehmann, Ed. P. J. Bickel, K. A. Docksum and J. L. Hodges, Jr., 157-84. Belmont CA: Wadsworth. Ibrahim, G. J. (1990). ”Incomplete data in generalized linear models”, American Statistical Association, 85, 765 - 769. Ibrahim, J. G. and Chen, M. H., Lipsitz, S. R., (1999). ”Monte Carlo EM for missing covariates in parametric regression models”, Biometrics, 55, 591 - 596. Little J. A. and Rubin D. B. (1987). Ststistical Analysis with Missing Data, New York: John Wiley & Sons. Little, J. A. and Schluchter, M. D. (1985). ”Maximum likelihood estimation for mixed continuous and categorical data with missing values”, Biometrika, 72, 497-512. Olkin, I., and Tate, R. F. (1961). ”Multivariate correlation models with mixed discrete and continuous variables”, Ann. Math. Statist., 32, 448-465. Pregibon, D. (1981). ”Logistic Regression Diagnostics”, The Annals of Statistic, 9 705-724. Rousseeuw, P. J. (1984). ”Least median of squares regression”, J. Am. Stat. Assoc., 79, 871-880. Rubin, D. B. (1976). ”Inference and missing data”, Biometrika 63, 581-592. Schafer, J. L. (1997). Analysis of Incomplete Multivariate Data, London: Chapman & Hall. Wei, G. C. and Tanner, M. A. (1990). ”A Monte Carlo implementation of the EM algorithm and the poor man’s data augmentation algorithm”. Journal of the American Statistical Association 85, 699-704. Zelterman, D. (1999). Models for Discrete Data, Oxford: Oxford University Press. |
描述: | 碩士 國立政治大學 統計研究所 90354008 91 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0090354008 | 資料類型: | thesis |
| Appears in Collections: | 學位論文 |
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