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題名 變數轉換之穩健迴歸分析
作者 張嘉璁
貢獻者 鄭宗記
張嘉璁
關鍵詞 Box-Cox乘冪轉換
前進演算法
最小中位數平方法
最小消去平方法
分數統計量
穩健迴歸
損壞點
離群值
Box-Cox power transformation
Forward search algorithm
Least median of squares
Least trimmed squares
Score statistic
Robust regression
Breakdown point
Outliers
日期 2001
上傳時間 15-Apr-2016 16:10:01 (UTC+8)
摘要 在傳統的線性迴歸分析當中，當基本假設不滿足時，有時可考慮變數轉換使得資料能夠比較符合基本假設。在眾多的轉換方法當中，以Box和Cox(1964)所提出的乘冪轉換(Box-Cox power transformation)最為常用，乘冪轉換可將某些複雜的系統轉換成線性常態模式。然而當資料存在離群值(outlier)時，Box-Cox Transformation會受到影響，因此不是一種穩健方法。
參考文獻 Andrews, D. F. (1974), “A Robust Method for Multiple Linear Regression” Technometrics 16, 523-31.
     Atkinson, A. C. (1973), “Testing Transformations to Normality” Journal of the Royal Statistical Society, Ser. B, 35, 473-479.
     ——— (1994), “Fast Very Robust Methods for the Detection of Multiple Outliers” Journal of the American Statistical Association, 89, 1329-1339.
     Atkinson, A. C., and Cheng, T. C. (1999), “Computing Least Trimmed Squares Regression with the Forward Search” Statistics and Computing, 9, 251-263.
     Box, G. E. P., and Cox, D. R. (1964), “An Analysis Of Transformations”(with discussion) Journal of the Royal Statistical Society, Ser. B, 26, 211-246.
     Brownlee, K. A. (1965), Statistical Theory and Methodology in Science and Engineering (2nd edn.). New York: Wiley.
     Daniel, C. and Wood, F. S. (1971), Fitting Equations to Data. New York: John Wiley.
     Donoho, D. L., and Huber, P. J. (1983), The notion of breakdown point, in A Festschrift for Erich Lehmann, edited by P. Bickel, K. Doksum, and J. L. Hodges, Jr., Wadsworth, Belmont, CA.
     Hawkins, D. M. (1994), “The Feasible Solution Algorithm for Least Trimmed Squares Regression” Computational Statistics and Data Analysis, 17, 185-196.
     Hoaglin, D. C., and Velleman, P. F. (1995), “A Critical Look at Some Analyses of Major League Baseball Salaries” The American Statistician, 49, 277-285.
     Rousseeuw, P. J. (1984), “Least Median of Squares Regression” Journal of the American Statistical Association, 79, 871-880.
     Rousseeuw, P. J., and Driessen, K. V. (1999), ”Computing LTS Regression for Large Data Sets”, Technical Report, University of Antwerp.
     Rousseeuw, P. J. and Leroy, A. M. (1987) Robust Regression and Outlier Detection, New York: John Wiley.
     Siegel, A. F. (1982), ”Robust Regression Using Repeated Medians,” Biometrika, 69, 242-244.
描述 碩士
國立政治大學
統計學系
88354005
資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001348
資料類型 thesis
dc.contributor.advisor 鄭宗記zh_TW
dc.contributor.author (Authors) 張嘉璁zh_TW
dc.creator (作者) 張嘉璁zh_TW
dc.date (日期) 2001en_US
dc.date.accessioned 15-Apr-2016 16:10:01 (UTC+8)-
dc.date.available 15-Apr-2016 16:10:01 (UTC+8)-
dc.date.issued (上傳時間) 15-Apr-2016 16:10:01 (UTC+8)-
dc.identifier (Other Identifiers) A2002001348en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/85135-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 88354005zh_TW
dc.description.abstract (摘要) 在傳統的線性迴歸分析當中，當基本假設不滿足時，有時可考慮變數轉換使得資料能夠比較符合基本假設。在眾多的轉換方法當中，以Box和Cox(1964)所提出的乘冪轉換(Box-Cox power transformation)最為常用，乘冪轉換可將某些複雜的系統轉換成線性常態模式。然而當資料存在離群值(outlier)時，Box-Cox Transformation會受到影響，因此不是一種穩健方法。zh_TW
dc.description.tableofcontents 封面頁
     證明書
     論文摘要
     1.前言
     2.變數轉換
     3.穩健迴歸估計
     4.實例分析
     5.結論與後續研究
     References		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001348en_US
dc.subject (關鍵詞) Box-Cox乘冪轉換zh_TW
dc.subject (關鍵詞) 前進演算法zh_TW
dc.subject (關鍵詞) 最小中位數平方法zh_TW
dc.subject (關鍵詞) 最小消去平方法zh_TW
dc.subject (關鍵詞) 分數統計量zh_TW
dc.subject (關鍵詞) 穩健迴歸zh_TW
dc.subject (關鍵詞) 損壞點zh_TW
dc.subject (關鍵詞) 離群值zh_TW
dc.subject (關鍵詞) Box-Cox power transformationen_US
dc.subject (關鍵詞) Forward search algorithmen_US
dc.subject (關鍵詞) Least median of squaresen_US
dc.subject (關鍵詞) Least trimmed squaresen_US
dc.subject (關鍵詞) Score statisticen_US
dc.subject (關鍵詞) Robust regressionen_US
dc.subject (關鍵詞) Breakdown pointen_US
dc.subject (關鍵詞) Outliersen_US
dc.title (題名) 變數轉換之穩健迴歸分析zh_TW
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Andrews, D. F. (1974), “A Robust Method for Multiple Linear Regression” Technometrics 16, 523-31.
     Atkinson, A. C. (1973), “Testing Transformations to Normality” Journal of the Royal Statistical Society, Ser. B, 35, 473-479.
     ——— (1994), “Fast Very Robust Methods for the Detection of Multiple Outliers” Journal of the American Statistical Association, 89, 1329-1339.
     Atkinson, A. C., and Cheng, T. C. (1999), “Computing Least Trimmed Squares Regression with the Forward Search” Statistics and Computing, 9, 251-263.
     Box, G. E. P., and Cox, D. R. (1964), “An Analysis Of Transformations”(with discussion) Journal of the Royal Statistical Society, Ser. B, 26, 211-246.
     Brownlee, K. A. (1965), Statistical Theory and Methodology in Science and Engineering (2nd edn.). New York: Wiley.
     Daniel, C. and Wood, F. S. (1971), Fitting Equations to Data. New York: John Wiley.
     Donoho, D. L., and Huber, P. J. (1983), The notion of breakdown point, in A Festschrift for Erich Lehmann, edited by P. Bickel, K. Doksum, and J. L. Hodges, Jr., Wadsworth, Belmont, CA.
     Hawkins, D. M. (1994), “The Feasible Solution Algorithm for Least Trimmed Squares Regression” Computational Statistics and Data Analysis, 17, 185-196.
     Hoaglin, D. C., and Velleman, P. F. (1995), “A Critical Look at Some Analyses of Major League Baseball Salaries” The American Statistician, 49, 277-285.
     Rousseeuw, P. J. (1984), “Least Median of Squares Regression” Journal of the American Statistical Association, 79, 871-880.
     Rousseeuw, P. J., and Driessen, K. V. (1999), ”Computing LTS Regression for Large Data Sets”, Technical Report, University of Antwerp.
     Rousseeuw, P. J. and Leroy, A. M. (1987) Robust Regression and Outlier Detection, New York: John Wiley.
     Siegel, A. F. (1982), ”Robust Regression Using Repeated Medians,” Biometrika, 69, 242-244.		zh_TW