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Complete convergence for weighted sums of random variables

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  • Sung, Soo Hak

Abstract

We obtain new complete convergence results for weighted sums of independent random variables. As a corollary, we obtain a result on the rate of convergence of moving average processes. Some well known results from the literature can be easily obtained from our results.

Suggested Citation

  • Sung, Soo Hak, 2007. "Complete convergence for weighted sums of random variables," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 303-311, February.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:3:p:303-311
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    References listed on IDEAS

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    1. Li, Deli & Bhaskara Rao, M. & Wang, Xiangchen, 1992. "Complete convergence of moving average processes," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 111-114, May.
    2. Sung, Soo Hak & Volodin, Andrei I. & Hu, Tien-Chung, 2005. "More on complete convergence for arrays," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 303-311, March.
    3. Hu, T. -C. & Szynal, D. & Volodin, A. I., 1998. "A note on complete convergence for arrays," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 27-31, May.
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    Cited by:

    1. Qiu, Dehua & Chen, Pingyan, 2014. "Complete moment convergence for i.i.d. random variables," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 76-82.
    2. Xuejun Wang & Chen Xu & Tien-Chung Hu & Andrei Volodin & Shuhe Hu, 2014. "On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 607-629, September.
    3. Wei Li & Pingyan Chen & Soo Hak Sung, 2016. "Complete Moment Convergence for Sung’s Type Weighted Sums of -Valued Random Elements," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-8, March.

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