臺灣博碩士論文加值系統

在樹狀方法中，我們透過變數選取之偏差與選取檢定力的模擬實驗來比較GUIDE和PARTY兩種迴歸樹的變數選取方法。模擬實驗裡我們變化自變數間的相關性去觀察兩方法選到各個自變數的機率估計值。從實驗的結果顯示， GUIDE方法在應變數與自變數間多項式關係為偶數次方時，其表現較佳；PARTY方法則在應變數與自變數間多項式關係為奇數次方時，其表現較佳，但PARTY方法在某些自變數存在相關性時，會產生選取偏差。

1 導論
2 變數選取方法
2.1 GUIDE方法 . . . . . . . . . . . . . . . . . . . . . 7
2.2 PARTY方法 . . . . . . . . . . . . . . . . . . . . . 9
3 模擬分析 14
3.1 變數選取之偏差 . . . . . . . . . . . . . . . . . . . . 15
3.1.1 自變數個數為二 . . . . . . . . . . . . . . . . 15
3.1.2 自變數個數為三 . . . . . . . . . . . . . . . . 16
3.1.3 自變數個數為四 . . . . . . . . . . . . . . . . 17
3.1.4 其中有一自變數取值為兩個 . . . . . . . . . . 19
3.1.5 其中有一自變數取值為四個 . . . . . . . . . . 20
3.2 選取檢定力 . . . . . . . . . . . . . . . . . . . . . . 22
4 結論 26

Breiman Li, Friedman J. H., Olshen R. A. and Stone, C. J. (1984), Classifi-
cation and Regression Trees, Belmont: Wadsworth.
Chaudhuri, P, Huang, M.-C., Loh, W.-Y., and Yao, R. (1994), “Piecewise-
polynomial regression trees”, Statistica Sinica, 4, 143–167.
Hawkins, Douglas M. (1991), “FIRM: Formal inference-based recursive mod-
eling”, The American Statistician, 45, 155–155.
Hothorn, T., Hornik, K., van de Wiel, Mark A., and Zeileis, A. (2006a),
“A lego system for conditional inference”, The American Statistician, 60,
257–263.
Hothorn, T., Hornik, K., and Zeileis, A. (2006b), “Unbiased recursive par-
titioning: A conditional inference framework”, Journal of Computational
and Graphical Statistics, 15, 651–674.
Li K.-C., Lue H.-H. and Chen, C.-H. (2000), “Interactive tree-structured
regression via principal hessian directions.”, Journal of the American Sta-
tistical Association., 95, 547–560.
Loh, W.-Y. (2002), “Regression trees with unbiased variable selection and
interaction detection”, Statistica Sinica, 12, 361–386.
Quinlan, J. R. (1992), Learning with continuous classes, in Proceedings of
the 5th Australian Joint Conference on Artificial Intelligence., 343–348,
Singapore: World Scientific.
R: A Language and Environment for Statistical Computing (2006),
R Foundation for Statistical Computing, Vienna, Austria, URL:
http://www.R-project.org, ISBN 3-900051-07-0.
Strasser, H. and Weber, C. (1999), “The asymptotic theory of permutation
statistics”, Mathematical Methods of Statistics, 8, 220–250.