A remark on LSL for weighted sums of i.i.d random elements

Pingyan Chen and Ran Chen

Statistics & Probability Letters, 2010, vol. 80, issue 17-18, 1329-1334

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].

Keywords: Law; of; the; single; logarithm; Random; element; Weighted; sums (search for similar items in EconPapers)
Date: 2010
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