LIL and the Approximation of Rectangular Sums of B-valued Random Variables when Extreme Terms are Excluded

作     者：Li Xin ZHANG Department of Mathematics Xixi Campus. Zhejiang University, Hangzhou 310028, P. R. China 

作者机构：Department of Mathematics Xixi Campus Zhejiang University Hangzhou P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2002年第18卷第3期

页      面：605-614页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China (No. 10071072) 

主　　题：Strong approximation Trimmed sums The law of iterated logarithm 

摘      要：Let {X, X_; ∈N^d} be a field of i.i.d, random variables indexed by d-tuples of positive integers and taking values in a Banach space B and let X_^((r))=X_(m) if ‖X_‖ is the r-th maximum of {‖X_‖; ≤. Let S_=∑(≤)X_ and ^((r))S_=S_-(X_^((1))+…+X_^((r)). We approximate the trimmed sums ^((r))_n, by a Brownian sheet and obtain sufficient and necessary conditions for ^((r))S_ to satisfy the compact and functional laws of the iterated logarithm. These results improve the previous works by Morrow (1981), Li and Wu (1989) and Ledoux and Talagrand (1990).