Chia Nan University of Pharmacy & Science Institutional Repository:Item 310902800/21998
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    Title: Approximation Theorems of the Empirical Distribution of the Sample Mean For Φ -Mixing Random Vectors
    Authors: Bih-Sheue Shieh
    Sheng-Kai Yang
    Contributors: 資訊管理系
    Keywords: weakly dependent random vectors
    invariant principle
    law of iterated logarithm
    Φ -mixing
    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).
    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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