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

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/7964

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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