Acta Scientiarum Naturalium Universitatis Pekinensis

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A Law of the Iterated Logarithm for the Heavily Trimmed Sums

WANG Fang,CHENG Shihong   

  1. Department of Probability and Statistics, School of Mathematical Sciences, Peking University, Beijing, 100871
  • Received:2000-04-19 Online:2001-05-20 Published:2001-05-20



  1. 北京大学数学学院概率统计系,北京,100871

Abstract: Let{Xn, n≥1} be a sequence of i.i.d. random variables with common d.f.F(x). X1, n≤…≤Xn, n}are its order statistics. Qis 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-λare continuity points of Q and σ(λ)>0. Moreover, a strong approximation result is obtained in this case.

Key words: heavily trimmed sums, LIL, strong approximation

摘要: 令{Xn, n≥1}是一列独立同分布的随机变量,其共同分布为F(x). X1, n≤…≤Xn, n}是其次序统计量。QF的分位函数。对任何分布函数F,只要λ和1-λQ 的连续点且σ(λ)>0,重截和的重对数律成立。而且在这种情形下获得了强逼近结果。

关键词: 重截和, 重对数律, 强逼近

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