Approximation Theorems of the Empirical Distribution of the Sample Mean For Φ -Mixing Random Vectors

CNU IR > Chna Nan Annual Bulletin > No.28 (2002) > Item 310902800/21998

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Title:	Approximation Theorems of the Empirical Distribution of the Sample Mean For Φ -Mixing Random Vectors Φ-混合隨機向量樣本平均之近似理論
Authors:	Bih-Sheue Shieh Sheng-Kai Yang
Contributors:	資訊管理系化妝品應用與管理系
Keywords:	weakly dependent random vectors invariant principle law of iterated logarithm Φ -mixing 弱相關隨機向量不變原則對數反覆律 Φ-混合
Date:	2003
Issue Date:	2010-03-24 16:45:17 (UTC+8)
Abstract:	Let {Xi:-∞I<i<∞} be a Φ-mixing stationary sequence of random vectors. Let Fn(x) be the corresponding empirical distribution function of X1,…,Xn,and let X ,be the sample mean of the present investigation is to show that the asymptotic almostsure representation of Fn(X). Two different orders of the remainder term,under different Φ-mixing conditions, are obtained and used for proving functional central limit theorrms, laws of iterated logarithm, Wiener processes embedding and invariant principles for Fn(X).
Relation:	嘉南學報 28期 : p.44-52
Appears in Collections:	[Chna Nan Annual Bulletin] No.28 (2002) [Dept. of Information Management] Periodical Articles [Dept. of Cosmetic Science and institute of cosmetic science] Periodical Articles

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