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題名 自變數增加對岭估計的影響分析
作者 萬世卿
Wan, Shin Chin
貢獻者 宋傳欽
萬世卿
Wan, Shin Chin
關鍵詞 岭估計
共線性
Cook統計量
AP統計量
Kullback-Leibler 對稱散度
變異膨脹因子
廣義變異膨脹因子
Ridge regression
日期 1998
上傳時間 27-Apr-2016 11:15:10 (UTC+8)
摘要 　　在最小平方估計中，當自變數間有共線性關係時，參數估計的變異變大，使得參數估計值不穩定。解決共線性對參數估計所造成影響的方法有很多，岭估計就是其中之一。在岭估計中，為了偵測出對岭估計有影響力的自變數，本文仿照Schall-Dunne的處理方式，推導出類似的Cook統計量及AP估計量，並且提出以Kullback-Leibler對稱散度來偵測對岭估計有影響力自變數。最後用"加拿大金融市場"與"員工對主管滿意度調查"的兩個實例，來說明本文所提出對岭估計有影響力自變數之偵測方法。
參考文獻 參考文獻
     [1] Andrews, D. F., and Pregibon, D.(1978),"Finding the Outliers That Matter,"Journal of The Royal Statistical Society, Ser. B, 40, 85-93.
     [2] Cook, R. D.(1977),"Detection of Influential Observations in Regression,"Technometrics, 19, 15-18.
     [3] Draper, N. R. and John, J. A.(1981),"Influential Observations and Outliers in Regression,"Technometrics, 23, 21-26.
     [4] Fox, J. and Monette, G.(1992),"Generalized Collinearity Diagnostics,"Journal of The American Statistical Association, 87, 178-183.
     [5] Graybill, F. A.(1976), Theory and Applications of the Linear Model, Duxbury, North Scitutate, Mass.
     [6] Hald, A.(1652), Statistical Theory With Engineering Applications, Wiley, new York.
     [7] Hoerl, A. E. and Kennard, R.W.(1970 a),"Ridge regression: Biased estimation for nonorthogonal problems,"Technometrics, 12, 55-67.
     [8] Hoerl, A. E. and Kennard, R.W.(1970 b),"Ridge regression: Applications to nonorthogonal problems," Technometrics, 12, 69-82.
     [9] Johnson, W. and Geisser, S.(1983),"A Predictive View of the Detection and Characterization of Influential Observations in Regression Analysis,"Journal of The American Statistical Association, 78, 137-144.
     [10] Jobson, J. D.(1991), Applied Multivariate Data Analysis Volume Ⅰ: Regression and Experimental Design, Academic: New York.
     [11] Kullback, S. and Leibler, R. A.(1951),"On Information and Sufficiency,"Annals of Mathematical Statistics, 22, 79-86.
     [12] Montgonery, D. C. and Peck, E. A.(1992), Introduction to Linear Regression Analysis (2nd ed), Academic: New York.
     [13] Schall, R. and Dunne, T. T.(1990),"Influential Variables in Linear Regression,"Technometrics, 32, 323-330.
     [14] Sen, A. K. and Srivastava, M. S.(1990), Regression Analysis Theory, Methods, and Applications, Academic: New York.
     [15] 岳榮先(1991)，"有偏估計的影響分析"，中國統計學報，第29卷第2期，219-231.
描述 碩士
國立政治大學
應用數學系
86751011
資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002001693
資料類型 thesis
dc.contributor.advisor 宋傳欽zh_TW
dc.contributor.author (Authors) 萬世卿zh_TW
dc.contributor.author (Authors) Wan, Shin Chinen_US
dc.creator (作者) 萬世卿zh_TW
dc.creator (作者) Wan, Shin Chinen_US
dc.date (日期) 1998en_US
dc.date.accessioned 27-Apr-2016 11:15:10 (UTC+8)-
dc.date.available 27-Apr-2016 11:15:10 (UTC+8)-
dc.date.issued (上傳時間) 27-Apr-2016 11:15:10 (UTC+8)-
dc.identifier (Other Identifiers) B2002001693en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/86270-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學系zh_TW
dc.description (描述) 86751011zh_TW
dc.description.abstract (摘要) 　　在最小平方估計中，當自變數間有共線性關係時，參數估計的變異變大，使得參數估計值不穩定。解決共線性對參數估計所造成影響的方法有很多，岭估計就是其中之一。在岭估計中，為了偵測出對岭估計有影響力的自變數，本文仿照Schall-Dunne的處理方式，推導出類似的Cook統計量及AP估計量，並且提出以Kullback-Leibler對稱散度來偵測對岭估計有影響力自變數。最後用"加拿大金融市場"與"員工對主管滿意度調查"的兩個實例，來說明本文所提出對岭估計有影響力自變數之偵測方法。zh_TW
dc.description.tableofcontents 謝詞
     摘要
     目錄
     第一章緒論-----1
     　　第一節：前言-----1
     　　第二節：本文架構-----2
     第二章　線性迴歸模型中偵測有影響力的自變數－文獻回顧-----3
     　　第一節：有影響力的個變數-----3
     　　第二節：廣義變異膨脹因子-----5
     　　第三節：Cook統計量-----7
     　　第四節：AP統計量-----9
     第三章　對岭估計有影響力的自變數之偵測-----11
     　　第一節：岭估計的介紹-----11
     　　第二節：偵測對岭估計有影響力自變數的Cook統計量-----12
     　　第三節：偵測對岭估計有影響力自變數的AP統計量-----15
     　　第四節：以Kullback-Leilber對稱散度偵測對岭估計有影響力的自變數-----17
     第四章　實例分析-----20
     　　第一節：實例說明與分析-----20
     　　第二節：結論-----25
     參考文獻-----37
     附錄-----39		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002001693en_US
dc.subject (關鍵詞) 岭估計zh_TW
dc.subject (關鍵詞) 共線性zh_TW
dc.subject (關鍵詞) Cook統計量zh_TW
dc.subject (關鍵詞) AP統計量zh_TW
dc.subject (關鍵詞) Kullback-Leibler 對稱散度zh_TW
dc.subject (關鍵詞) 變異膨脹因子zh_TW
dc.subject (關鍵詞) 廣義變異膨脹因子zh_TW
dc.subject (關鍵詞) Ridge regressionen_US
dc.title (題名) 自變數增加對岭估計的影響分析zh_TW
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 參考文獻
     [1] Andrews, D. F., and Pregibon, D.(1978),"Finding the Outliers That Matter,"Journal of The Royal Statistical Society, Ser. B, 40, 85-93.
     [2] Cook, R. D.(1977),"Detection of Influential Observations in Regression,"Technometrics, 19, 15-18.
     [3] Draper, N. R. and John, J. A.(1981),"Influential Observations and Outliers in Regression,"Technometrics, 23, 21-26.
     [4] Fox, J. and Monette, G.(1992),"Generalized Collinearity Diagnostics,"Journal of The American Statistical Association, 87, 178-183.
     [5] Graybill, F. A.(1976), Theory and Applications of the Linear Model, Duxbury, North Scitutate, Mass.
     [6] Hald, A.(1652), Statistical Theory With Engineering Applications, Wiley, new York.
     [7] Hoerl, A. E. and Kennard, R.W.(1970 a),"Ridge regression: Biased estimation for nonorthogonal problems,"Technometrics, 12, 55-67.
     [8] Hoerl, A. E. and Kennard, R.W.(1970 b),"Ridge regression: Applications to nonorthogonal problems," Technometrics, 12, 69-82.
     [9] Johnson, W. and Geisser, S.(1983),"A Predictive View of the Detection and Characterization of Influential Observations in Regression Analysis,"Journal of The American Statistical Association, 78, 137-144.
     [10] Jobson, J. D.(1991), Applied Multivariate Data Analysis Volume Ⅰ: Regression and Experimental Design, Academic: New York.
     [11] Kullback, S. and Leibler, R. A.(1951),"On Information and Sufficiency,"Annals of Mathematical Statistics, 22, 79-86.
     [12] Montgonery, D. C. and Peck, E. A.(1992), Introduction to Linear Regression Analysis (2nd ed), Academic: New York.
     [13] Schall, R. and Dunne, T. T.(1990),"Influential Variables in Linear Regression,"Technometrics, 32, 323-330.
     [14] Sen, A. K. and Srivastava, M. S.(1990), Regression Analysis Theory, Methods, and Applications, Academic: New York.
     [15] 岳榮先(1991)，"有偏估計的影響分析"，中國統計學報，第29卷第2期，219-231.		zh_TW