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題名 改良式脊迴歸分析法於預測模式之應用
Applied Improved Ridge Regression Analysis
作者 周玫芳
Chou, Mei Fang
貢獻者 謝邦昌
Shia, Ben Chang
周玫芳
Chou, Mei Fang
關鍵詞 脊迴歸
刀削法
偏量估計式
Ridge Regression
Jackknife
Biased estimator
日期 1994
1993
上傳時間 29-Apr-2016 15:31:04 (UTC+8)
摘要 當我們在應用迴歸分析法時，往往會遇到兩個或多個自變數間存在著線性
參考文獻 1.林燦隆、謝邦昌、唐榮澤，(1989)，利用氣象因子建立甘
蔗糖份含量之預測模式，台灣糖業研究所研究彙報，
124:1-12

2.鄭敏祿，(1985)，脊廻歸估計之模擬研究。國立政治大
學統計學研究所碩士論文。

3.謝邦昌，(1991)，綜合預測模式之探討－甘蔗蔗產量及
糖份含量依氣象因子二段式加權預測模式之研究。國立台
灣大學農藝學研究所生物統計組博士論文。


4. Brown, W.G. and Beattie, B.R. (1975).Improving Estimates Of Economic Parameters By Use Of Ridge Regression With Production Function Applications. Am.J.Agric.Econ.,57,21-32

5. Douglas, G.F.(1978).Ridge Regression:When Biased Estimation Is Better, Social Science Ouarterly, Vol.58,No.4,March: 708-716

6. Draper, N. R. and Smith , H. (1981). Applied Regression Analysis, Second Edition, New York.

7.Ellen ,B.R.(1991). Prediction Error and Its Estimation for Subset-Selected Models, Technometrics, Vol.33, No.4,November:459-467

8.Hinkley, D.V. (1977). Jackknifing In Unbalanced Situations, Technometrics, Vol.19,No.3,August:285-292

9.Hoerl, A.E. and Kennard, R.W. (1970). Ridge Regression : Biased Estimation For Nonorthogonal Problems, Technometrics, Vol.12, No.1, February:55-67

10. Hoerl, A.E. and Kennard, R.W. (1970). Ridge Regression : Applications to Nonorthogonal Problems , Technometrics, Vol.12, No.1, February:69-83

11. Hoerl, A.E. Kennard, R.W. and Baldwin,K.F.(1975) Ridge Regression: Some Simulations, Communications In Statistics, 4(2), 105-123

12.Hoerl,A.E. and Kennard,R.W.(1976).Ridge Regression : Iterative Estimation Of The Biased Parameter, Commun.Statis. Theor. Meth.A5(1):77-88

13.John Neter, (1989). Applied Linear Regression Models, Second Edition, Boston.

14.Loesgen,K.H.(1990). Generalization and Bayesian Interpretation of Ridge-Type Estimators with Good Prior Means, Statistical Papers, 31:147-157

15.McDonald ,G.C. and Galarneau,D.I. (1975). A Monte Carlo evaluation of Some Ridge Type estimators.JASA,70:407-416

16.Miller,R.G. (1968) Jackkinfing Variance. Ann.Math.Stqtist.,39:567-582

17.Miller,R.G. (1974). An Unbalanced Jackknife, The Annals Of Statistics, Vol 2, No.5:880-891

18.Nityananda Sarkar, (1992), A New Estimator Combining The Ridge Regression And The Restricted Least Squares Methods Of Estimation, Commun. Statist. Theory Meth.,21(7):1987-2000

19.Nordberg, L. (1982). A Procedure For Determination Of A Good Ridge Parameter In Linear Regression. Commun. Statist. B11:285-309

20.Quenouille,M.H.(1956).Note On Bias In Estimation. Biometrika. 43:353-360

21.SAS/IML User’s Guide.(1985). SAS Institute Inc. North Carolina.
22.Segerstedt,B.(1992).On Ordinary Ridge Regression In Generalized Linear Models, Commun.Statist.-Theory Meth., 21(8):2227-2246

23.Shao,J. and Wu,C.F.J. (1987), Heterpscedastocoty-Robustness Of Jackknife Variance Estimators In Linear Models, The Annals Of Statistics, Vol.15 ,No. 4:1563-1579

24.Shao,J.(1992).Jackknifing In Generalized Linear Models, Ann.Inst. Statist. Math. Vol.44,No. 4,673-686

25. Turkey, J.W. (1958) Bias And Confidence In Not-Quite Large Samples. Ann.Math.Statist.,29:614
描述 碩士
國立政治大學
統計學系
81354014
資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002003827
資料類型 thesis
dc.contributor.advisor 謝邦昌zh_TW
dc.contributor.advisor Shia, Ben Changen_US
dc.contributor.author (Authors) 周玫芳zh_TW
dc.contributor.author (Authors) Chou, Mei Fangen_US
dc.creator (作者) 周玫芳zh_TW
dc.creator (作者) Chou, Mei Fangen_US
dc.date (日期) 1994en_US
dc.date (日期) 1993en_US
dc.date.accessioned 29-Apr-2016 15:31:04 (UTC+8)-
dc.date.available 29-Apr-2016 15:31:04 (UTC+8)-
dc.date.issued (上傳時間) 29-Apr-2016 15:31:04 (UTC+8)-
dc.identifier (Other Identifiers) B2002003827en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/88359-
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) 81354014zh_TW
dc.description.abstract (摘要) 當我們在應用迴歸分析法時，往往會遇到兩個或多個自變數間存在著線性zh_TW
dc.description.tableofcontents 第 一 章 緒論
1-1 研究緣起………………………………………………………………………………………………………….1
1-2 研究動機與目的……………………………………………………..……………………………………….2
1-3 研究方法及架構…………………………..………………………………………………………………….8
第 二 章 前人研究
2-1 脊迴歸方面之文獻探討………………………………………………………………….…….………….9
2-2 Jackknife估計法之文獻探討…………………………………………………….……………….….11
2-3 改良式脊迴歸分析法之文獻探討……………………………………………….………………….13
第 三 章 理論方法
3-1 脊迴歸分析……………………………………………………………………………….…………………….14
3-2 Jackknife取一法………………………………………………..………………………………………….23
3-3 改良式脊迴歸估計法……………………………………………………………….…………………….29
第 四 章 實例探討與模擬研究
4-1 實例探討…………………………………………………………………………….………………….……….34
4-2 電腦模擬………………………………………………………………………….…………………….……….38
4-3 模擬結果……………………………………………………………………….……………………….……….41
第 五 章 結論………………………………………….…………………………………….…………….53
參考文獻……………………………………………………………………………………..……………..………….56
附錄一 SAS/IML程式……………………………………….……..…………………………………….59
附錄二 實例探討之原始資料及輸出結果…………………………………………………….62

表目錄

表 一 傳統脊估式與改良式脊估式預測能力之比較……………………..…………..………35
表 二 Jackknife取一法n個估計系數………………………………………………………….………36
表 三 r² = 0.1傳統脊估式與改良式脊估式之比較分析………………..…………..………43
表 四 r² = 0.3傳統脊估式與改良式脊估式之比較分析……………………..……..………44
表 五 r² = 0.5傳統脊估式與改良式脊估式之比較分析…………………………....………45
表 六 r² = 0.7傳統脊估式與改良式脊估式之比較分析……………………..……..………46
表 七 r² = 0.9傳統脊估式與改良式脊估式之比較分析………..……………….….………47
表 八 傳統脊估式與改良式脊估式之比較分析……………………………….…………………48

圖目錄

圖 一 bR 與b之抽樣分配……………………………………………………………………………………14
圖 二 傳統脊估式與改良式脊估式的預測情形……………………………………….…………35
圖 三 r² = 0.1 Td²與I d²之比較……………………………………………………..………………………49
圖 四 r² = 0.3 Td²與I d²之比較………………………………………..……………………………………49
圖 五 r² = 0.5 Td²與I d²之比較…………………………………………………………………………..…50
圖 六 r² = 0.7 Td²與I d²之比較…………………………………………………..…………………………50
圖 七 r² = 0.9 Td²與I d²之比較……………………………………………………………………………..51
圖 八 不同共線性下兩估計式之bias²…………………………………………………………………51
圖 九 不同共線性下兩估計式之MSE…………………………………………………………………52
圖 十 不同共線性下兩估計式之bias²與MSE…………………………………………………….52		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002003827en_US
dc.subject (關鍵詞) 脊迴歸zh_TW
dc.subject (關鍵詞) 刀削法zh_TW
dc.subject (關鍵詞) 偏量估計式zh_TW
dc.subject (關鍵詞) Ridge Regressionen_US
dc.subject (關鍵詞) Jackknifeen_US
dc.subject (關鍵詞) Biased estimatoren_US
dc.title (題名) 改良式脊迴歸分析法於預測模式之應用zh_TW
dc.title (題名) Applied Improved Ridge Regression Analysisen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 1.林燦隆、謝邦昌、唐榮澤，(1989)，利用氣象因子建立甘
蔗糖份含量之預測模式，台灣糖業研究所研究彙報，
124:1-12

2.鄭敏祿，(1985)，脊廻歸估計之模擬研究。國立政治大
學統計學研究所碩士論文。

3.謝邦昌，(1991)，綜合預測模式之探討－甘蔗蔗產量及
糖份含量依氣象因子二段式加權預測模式之研究。國立台
灣大學農藝學研究所生物統計組博士論文。


4. Brown, W.G. and Beattie, B.R. (1975).Improving Estimates Of Economic Parameters By Use Of Ridge Regression With Production Function Applications. Am.J.Agric.Econ.,57,21-32

5. Douglas, G.F.(1978).Ridge Regression:When Biased Estimation Is Better, Social Science Ouarterly, Vol.58,No.4,March: 708-716

6. Draper, N. R. and Smith , H. (1981). Applied Regression Analysis, Second Edition, New York.

7.Ellen ,B.R.(1991). Prediction Error and Its Estimation for Subset-Selected Models, Technometrics, Vol.33, No.4,November:459-467

8.Hinkley, D.V. (1977). Jackknifing In Unbalanced Situations, Technometrics, Vol.19,No.3,August:285-292

9.Hoerl, A.E. and Kennard, R.W. (1970). Ridge Regression : Biased Estimation For Nonorthogonal Problems, Technometrics, Vol.12, No.1, February:55-67

10. Hoerl, A.E. and Kennard, R.W. (1970). Ridge Regression : Applications to Nonorthogonal Problems , Technometrics, Vol.12, No.1, February:69-83

11. Hoerl, A.E. Kennard, R.W. and Baldwin,K.F.(1975) Ridge Regression: Some Simulations, Communications In Statistics, 4(2), 105-123

12.Hoerl,A.E. and Kennard,R.W.(1976).Ridge Regression : Iterative Estimation Of The Biased Parameter, Commun.Statis. Theor. Meth.A5(1):77-88

13.John Neter, (1989). Applied Linear Regression Models, Second Edition, Boston.

14.Loesgen,K.H.(1990). Generalization and Bayesian Interpretation of Ridge-Type Estimators with Good Prior Means, Statistical Papers, 31:147-157

15.McDonald ,G.C. and Galarneau,D.I. (1975). A Monte Carlo evaluation of Some Ridge Type estimators.JASA,70:407-416

16.Miller,R.G. (1968) Jackkinfing Variance. Ann.Math.Stqtist.,39:567-582

17.Miller,R.G. (1974). An Unbalanced Jackknife, The Annals Of Statistics, Vol 2, No.5:880-891

18.Nityananda Sarkar, (1992), A New Estimator Combining The Ridge Regression And The Restricted Least Squares Methods Of Estimation, Commun. Statist. Theory Meth.,21(7):1987-2000

19.Nordberg, L. (1982). A Procedure For Determination Of A Good Ridge Parameter In Linear Regression. Commun. Statist. B11:285-309

20.Quenouille,M.H.(1956).Note On Bias In Estimation. Biometrika. 43:353-360

21.SAS/IML User’s Guide.(1985). SAS Institute Inc. North Carolina.
22.Segerstedt,B.(1992).On Ordinary Ridge Regression In Generalized Linear Models, Commun.Statist.-Theory Meth., 21(8):2227-2246

23.Shao,J. and Wu,C.F.J. (1987), Heterpscedastocoty-Robustness Of Jackknife Variance Estimators In Linear Models, The Annals Of Statistics, Vol.15 ,No. 4:1563-1579

24.Shao,J.(1992).Jackknifing In Generalized Linear Models, Ann.Inst. Statist. Math. Vol.44,No. 4,673-686

25. Turkey, J.W. (1958) Bias And Confidence In Not-Quite Large Samples. Ann.Math.Statist.,29:614		zh_TW