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 Title: 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 Authors: 陳盈安;Ying-an Chen Contributors: 數學研究所 Keywords: 對稱型機率密度函數;Kernel Estimators;Symmetric Probability Density Functions Date: 2009-05-21 Issue Date: 2009-09-22 11:10:20 (UTC+8) Publisher: 國立中央大學圖書館 Abstract: 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. 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. Appears in Collections: [Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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