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| Title: | SIR、SAVE、SIR-II、pHd等四種維度縮減方法之比較探討 |
| Authors: | 方悟原
Fang, Wu-Yuan |
| Contributors: | 江振東
方悟原
Fang, Wu-Yuan |
| Keywords: | 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 |
| Date: | 1998 |
| Issue Date: | 2016-04-21 09:54:36 (UTC+8) |
| Abstract: | 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). |
| Reference: | 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 |
| Description: | 碩士
國立政治大學
統計學系
84354014 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#B2002001549 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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