Asymptotic Representation of The Proportion of The Sample Below The Sample Mean For Φ -mixing Random Variables

CNU IR > Chna Nan Annual Bulletin > Vol.25 (1999) > Item 310902800/22533

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Title:	Asymptotic Representation of The Proportion of The Sample Below The Sample Mean For Φ -mixing Random Variables 關於Φ -混合隨機變數中低於樣本平均之樣本比例近似表現理論
Authors:	Chung-Wen Chang Wen-Sz Chiue Bih-Sheue Shieh
Contributors:	化妝品應用管理系資訊管理系
Keywords:	Φ -mixing stationary almost sure representation weak dependent law of iterated logarithm invariant priciple Φ -混合幾乎處處弱相關對數反覆律不變原理中央極限
Date:	1999
Issue Date:	2010-04-08 13:04:42 (UTC+8)
Abstract:	Let {Xi:-∞<i<∞}be a stationary sequence of random variables. Let Fn(x) be the corresponding empirical distribution function of X1,…,Xn,and let X=Σi=1 Xi/n be the sample mean. In this paper,we derive the asymptotic almost sure representation, the central limit theorem, a law of iterated logarithm, a Wiener process embedding and an invariant principle for Fn(X) under different Φ-mixing conditios. 設{xi :-∞<i<∞} 為一穩定的隨機變數序例，Fn(x)為對應X1，…，Xn的經驗累積分配函數，X為x1，…， Xn的樣本平均。此論文中，我們導出在不同Φ-混合情況下， Fn(X)的幾乎處處近似表現，中央極限理論，對數反覆律，Wiener隨機對應和不變原理等性質。
Relation:	嘉南學報 25 : p.178-184
Appears in Collections:	[Chna Nan Annual Bulletin] Vol.25 (1999) [Dept. of Cosmetic Science and institute of cosmetic science] Periodical Articles [Dept. of Information Management] Periodical Articles

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