1. NCCU Academic Hub
  2. 學術產出
  3. College of Commerce
  4. Theses
  5. Item

學術產出-Theses

Article View/Open

Publication Export

Google ScholarTM

政大圖書館

Citation Infomation

  • No doi shows Citation Infomation
題名 SIR、SAVE、SIR-II、pHd等四種維度縮減方法之比較探討
作者 方悟原
Fang, Wu-Yuan
貢獻者 江振東
方悟原
Fang, Wu-Yuan
關鍵詞 維度縮減子空間
dimension reduction subspace
pHd
principal Hessian directions
SIR
sliced inverse regression
SAVE
sliced average variance estimate
SIR-II
日期 1998
上傳時間 21-Apr-2016 09:54:36 (UTC+8)
摘要 本文以維度縮減(dimension reduction)為主題，介紹其定義以及四種目前較被廣為討論的處理方式。文中首先針對Li (1991)所使用的維度縮減定義型式y = g(x,ε) = g1(βx,ε)，與Cook (1994)所採用的定義型式「條件密度函數f(y | x)=f(y |βx)」作探討，並就Cook (1994)對最小維度縮減子空間的相關討論作介紹。此外文中也試圖提出另一種適用於pHd的可能定義(E(y | x)=E(y |βx)，亦即縮減前後y的條件期望值不變)，並發現在此一新定義下所衍生而成的子空間會包含於Cook (1994)所定義的子空間。
The focus of the study is on the dimension reduction and the over-view of the four methods frequently cited in the literature, i.e. SIR, SAVE, SIR-II, and pHd. The definitions of dimension reduction proposed by Li (1991)(y = g( x,ε) = g1(βx,ε)), and by Cook (1994)(f(y | x)=f(y|βx)) are briefly reviewed. Issues on minimum dimension reduction subspace (Cook (1994)) are also discussed. In addition, we propose a possible definition (E(y | x)=E(y |βx)), i.e. the conditional expectation of y remains the same both in the original subspace and the reduced subspace), which seems more appropriate when pHd is concerned. We also found that the subspace induced by this definition would be contained in the subspace generated based on Cook (1994).
參考文獻 Chen, C. H., Li, K. C. (1998). Generalization of Fisher`s linear discriminant analysis via the approach of sliced inverse regression. Technical Report C-98-15, Institute of Statistical Science Academia Sinica, Taiwan, R.O.C.
     Chen, C. H., Li, K. C., Wang, J. L. (1999). Dimension reduction and censored regression. Annals of Statistics (to be appeared)
     Cook, R. D. (1994). On the interpretation of regression polts. Journal of the American Statistical Association, vol.89 p.177~189
     Cook, R. D., Weisberg, S. (1991). Comment on Li (1991). Journal of the American Statistical Association, vol.86 p.328~332
     Cook, R. D., Weisberg, S. (1994). An the introduction to regression gaphics. New York: Wiley
     Li, K. C. (1991). Sliced inverse regression for dimension reduction (with discussion). Journal of the American Statistical Association, vol.86 p.316~342
     Li, K. C. (1992). On principal Hessian directions for data visualization and dimension reduction : Another application of Stein`s lemma. Journal of the American Statistical Association, vol.87 p.1025~ 1039
     Schott, J. R. (1994). Determining the dimensionality of sliced inverse regression. Journal of the American Statistical Association, vol.89, p.141~148.
     Searle, S. R. (1982). Matrix algebra usejul for statistics. New York: Wiley
描述 碩士
國立政治大學
統計學系
84354014
資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002001549
資料類型 thesis
dc.contributor.advisor 江振東zh_TW
dc.contributor.author (Authors) 方悟原zh_TW
dc.contributor.author (Authors) Fang, Wu-Yuanen_US
dc.creator (作者) 方悟原zh_TW
dc.creator (作者) Fang, Wu-Yuanen_US
dc.date (日期) 1998en_US
dc.date.accessioned 21-Apr-2016 09:54:36 (UTC+8)-
dc.date.available 21-Apr-2016 09:54:36 (UTC+8)-
dc.date.issued (上傳時間) 21-Apr-2016 09:54:36 (UTC+8)-
dc.identifier (Other Identifiers) B2002001549en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/85878-
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) 84354014zh_TW
dc.description.abstract (摘要) 本文以維度縮減(dimension reduction)為主題，介紹其定義以及四種目前較被廣為討論的處理方式。文中首先針對Li (1991)所使用的維度縮減定義型式y = g(x,ε) = g1(βx,ε)，與Cook (1994)所採用的定義型式「條件密度函數f(y | x)=f(y |βx)」作探討，並就Cook (1994)對最小維度縮減子空間的相關討論作介紹。此外文中也試圖提出另一種適用於pHd的可能定義(E(y | x)=E(y |βx)，亦即縮減前後y的條件期望值不變)，並發現在此一新定義下所衍生而成的子空間會包含於Cook (1994)所定義的子空間。zh_TW
dc.description.abstract (摘要) The focus of the study is on the dimension reduction and the over-view of the four methods frequently cited in the literature, i.e. SIR, SAVE, SIR-II, and pHd. The definitions of dimension reduction proposed by Li (1991)(y = g( x,ε) = g1(βx,ε)), and by Cook (1994)(f(y | x)=f(y|βx)) are briefly reviewed. Issues on minimum dimension reduction subspace (Cook (1994)) are also discussed. In addition, we propose a possible definition (E(y | x)=E(y |βx)), i.e. the conditional expectation of y remains the same both in the original subspace and the reduced subspace), which seems more appropriate when pHd is concerned. We also found that the subspace induced by this definition would be contained in the subspace generated based on Cook (1994).en_US
dc.description.tableofcontents 第 一 章 前言••••••••••••••••••••• 1
      第1-1節 維度縮減的目的••••••••••••••• 1
      第1-2節 文獻回顧與章節提要•••••••••••• 3
     第 二 章 維度縮減定義的探討•••••••••••••• 4
      第2-1節 維度縮減的定義••••••••••••••• 4
      第2-2節 最小維度縮減子空間的探討••••••••••• 12
      第2-3節 維度縮減的另一種可能定義••••••••••• 15
     第 三 章 切片逆迴歸(SIR)運用於維度縮減的探討••••••• 17
      第3-1節 切片逆迴歸(SIR)的理論與性質•••••••••• 17
      第3-2節 切片逆迴歸(SIR)理論的另一種詮釋方式與
      缺失探討•••••••••••••••••• 23
     第 四 章 SAVE、SIR-II、pHd三種方法的介紹•••••••• 28
      第4-1節 多維常態下的性質••••••••••••••• 28
      第4-2節 SAVE的介紹••••••••••••••••• 31
      第4-3節 SIR-II的介紹••••••••••••••••• 37
      第4-4節 pHd的介紹••••••••••••••••• 43
     第 五 章 四種方法的比較與後續可能研究方向•••••••• 48
      第5-1節 SIR、SAVE、SIR-II、pHd四種方法的比較••••• 48
      第5-2節後續可能研究方向••••••••••••••• 50
     參考書目••••••••••••••••••••••• 52
     附 錄•••••••••••••••••••••••• 53		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002001549en_US
dc.subject (關鍵詞) 維度縮減子空間zh_TW
dc.subject (關鍵詞) dimension reduction subspaceen_US
dc.subject (關鍵詞) pHden_US
dc.subject (關鍵詞) principal Hessian directionsen_US
dc.subject (關鍵詞) SIRen_US
dc.subject (關鍵詞) sliced inverse regressionen_US
dc.subject (關鍵詞) SAVEen_US
dc.subject (關鍵詞) sliced average variance estimateen_US
dc.subject (關鍵詞) SIR-IIen_US
dc.title (題名) SIR、SAVE、SIR-II、pHd等四種維度縮減方法之比較探討zh_TW
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Chen, C. H., Li, K. C. (1998). Generalization of Fisher`s linear discriminant analysis via the approach of sliced inverse regression. Technical Report C-98-15, Institute of Statistical Science Academia Sinica, Taiwan, R.O.C.
     Chen, C. H., Li, K. C., Wang, J. L. (1999). Dimension reduction and censored regression. Annals of Statistics (to be appeared)
     Cook, R. D. (1994). On the interpretation of regression polts. Journal of the American Statistical Association, vol.89 p.177~189
     Cook, R. D., Weisberg, S. (1991). Comment on Li (1991). Journal of the American Statistical Association, vol.86 p.328~332
     Cook, R. D., Weisberg, S. (1994). An the introduction to regression gaphics. New York: Wiley
     Li, K. C. (1991). Sliced inverse regression for dimension reduction (with discussion). Journal of the American Statistical Association, vol.86 p.316~342
     Li, K. C. (1992). On principal Hessian directions for data visualization and dimension reduction : Another application of Stein`s lemma. Journal of the American Statistical Association, vol.87 p.1025~ 1039
     Schott, J. R. (1994). Determining the dimensionality of sliced inverse regression. Journal of the American Statistical Association, vol.89, p.141~148.
     Searle, S. R. (1982). Matrix algebra usejul for statistics. New York: Wiley		zh_TW