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Complete Moment Convergence for Sung’s Type Weighted Sums of -Valued Random Elements

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  • Wei Li
  • Pingyan Chen
  • Soo Hak Sung

Abstract

Let and Let be a sequence of independent and identically distributed -valued random elements and let be an array of real numbers satisfying for some We give necessary and sufficient conditions for complete moment convergence of the form , where A strong law of large numbers for weighted sums of independent -valued random elements is also obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnddns:1484160
    DOI: 10.1155/2016/1484160
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    References listed on IDEAS

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    1. 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.
    2. Bai, Z. D. & Cheng, Philip E., 2000. "Marcinkiewicz strong laws for linear statistics," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 105-112, January.
    3. Sung, Soo Hak, 2007. "Complete convergence for weighted sums of random variables," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 303-311, February.
    4. Soo Sung, 2011. "On the strong convergence for weighted sums of random variables," Statistical Papers, Springer, vol. 52(2), pages 447-454, May.
    5. Wu, Wei Biao, 1999. "On the strong convergence of a weighted sum," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 19-22, August.
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