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Almost Sure Central Limit Theorems for Heavily Trimmed Sums

Authors:	Email author" target="_blank">Fang?Wang Email author Shi?Hong?Cheng

Institution:	(1) Department of Mathematics, Capital Normal University, Beijing 100037, P. R. China;(2) Department of Probability and Statistics, Peking University, Beijing 100871, P. R. China

Abstract:	We obtain an almost sure central limit theorem (ASCLT) for heavily trimmed sums. We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums of i.i.d. random variables with $EX_{1} = 0,EX^{2}_{1} = 1$ . Supported by the National Natural Science Foundation of China (No. 10071003) and Beijing Municipal Education Commission (KM200310028107)

Keywords:	Almost sure central limit theorem Heavily trimmed sums Quantile-transform
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