A remark on LSL for weighted sums of i.i.d random elements |
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Authors: | Pingyan Chen Ran Chen |
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Institution: | 1. Department of Mathematics, Jinan University, Guangzhou, 510630, PR China;2. Department of Statistics, Jinan University, Guangzhou, 510630, PR China |
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Abstract: | In the paper, the upper bound and lower bound of the law of the single logarithm (LSL) are established under the condition that the sequence of the normalized weighted sums of random elements is bounded in probability. The main result improves the upper bound in Sung, S.H., 2009. A law of the single logarithm for weighted sums of i.i.d. random elements. Statist. Probab. Lett., 79, 1351–1357] and hence extends the result in Chen, P., Gan, S., 2007. Limiting behavior of weighted sums of i.i.d. random variables. Statist. Probab. Lett., 77, 1589–1599]. |
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