A law of the iterated logarithm for the heavily trimmed sums

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作者：
Wang, F. [1 ]
Cheng, S. [1 ]
机构：
[1] Dept. of Probability and Statistics, School of Mathematical Sciences, Peking University, Beijing, 100871, China
来源：
Beijing Daxue Xuebao Ziran Kexue Ban/Acta Scientiarum uaturalium Universitatis Pekinensis | 2001年 / 37卷 / 03期
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摘要：
Let {Xn, n greater than or equal 1} be a sequence of i.i.d. random variables with common d.f. F(x). X1,n [less-than or equal to] ... [less-than or equal to] Xn,n are its order statistics. Q is the quantile function of F. It is shown that for any underlying distribution function F, the LIL for the heavily trimmed sums remains true, as long as λ and 1 - λ are continuity points of Q and σ(λ) > 0. Moreover, a strong approximation result is obtained in this case.
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页码：289 / 293
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