LIL and the Approximation of Rectangular Sums of B-valued Random Variables when Extreme Terms are Excluded |
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| Authors: | Li Xin Zhang |
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| Institution: | (1) Department of Mathematics Xixi Campus, Zhejiang University, Hangzhou 310028, P. R. China, E-mail: lxzhang@mail.hz.zj.cn, CN |
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| Abstract: | Let 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 if is the r-th maximum of . Let and . We approximate the trimmed sums by a Brownian sheet and obtain sufficient and necessary conditions for 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).
Received March 22, 1999, Accepted October 13, 2000 |
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| Keywords: | Strong approximation Trimmed sums The law of iterated logarithm |
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