| 姓名 |
陳盈安(Ying-an Chen)
查詢紙本館藏 |
畢業系所 |
數學系 |
| 論文名稱 |
對稱型機率密度函數之一些泛函的核估計
(Kernel Estimators for Some Functionals of Symmetric Probability Density Functions)
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| 摘要(中) |
令X_1，X_2…X_n表一組獨立同分布之隨機變數且其共同機率密度函數為f(x)，則常用之f(x)之估計式為核估計式$hat{f}(x)$. 核估計式具有許多好的性質，密度函數之泛函如密度函數之眾數(mode)，微分及積分均有深入之研究( 參考 Pagan and Ullah (1999) , Silverman (1986) , Prakasa Rao (1983)及Tapia and Thompson (1977) ) . 本文研究對稱型機率密度函數 之一些尚未討論之泛函H(f)的核估計$H(hat{f})$，即關鍵點，反曲點，斜率，曲率及概似函數之核估計.
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| 摘要(英) |
Kernal density estimator $hat{f}$ is by far the most popular estimator of probability density function f .It is interesting to find performances of $H(hat{f})$ for functionals H(f) of f.Well known results cover a great many H(f) include $f^{(k)}(x)$
, the k-th derivatives of f,integral of f like $int_{-infty}^{x}f(s)ds$ , the distribution function , evaluated at x , and modes of x . In this paper , we investigate $H(hat{f})$ for functionals
H(f) that represent critical points and reflection points of f , slopes and curvatures of f evaluated at fixed points , and likelihood functions , topics that are not discussed yet.
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| 關鍵字(中) |
★ 核估計
★ 對稱型機率密度函數 |
關鍵字(英) |
★ Kernel Estimators
★ Symmetric Probability Density Functions |
| 論文目次 |
第一節 簡介.....................................1
第二節 關鍵點及反曲點之核估計...................2
第三節 斜率及曲率之核估計......................11
第四節 概似函數之核估計........................26
第五節 結論....................................33
參考文獻.......................................38
附錄A..........................................39
附錄B..........................................45
附錄C..........................................71
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| 參考文獻 |
[1] Lehmann，E.L. (1986) . Testing Statistical Hypotheses . 2nd ed. Wiley.
[2] Pagan , A. and Ullah , A. (1999) . Nonparametric Econometrics , Cambridge
University Press.
[3] Prakasa Rao , B.L.S (1983) . Nonparametric Functional Estimation . Academic
Press.
[4] Silverman , B.W. (1986) . Density Estimation for Statistics and Data Analysis ,
Chapman and Hall.
[5] Tapia , R.A. and Thompson , J.R. (1977) . Nonparametric Probability Density
Estimation . Johns Hopkins University Press.
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| 指導教授 |
許玉生(Yu-Sheng Hsu)
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審核日期 |
2009-6-5 |
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