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On Strong Convergence for Weighted Sums of a Class of Random Variables

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  • Aiting Shen

Abstract

Let {Xn, n ≥ 1} be a sequence of random variables satisfying the Rosenthal‐type maximal inequality. Complete convergence is studied for linear statistics that are weighted sums of identically distributed random variables under a suitable moment condition. As an application, the Marcinkiewicz‐Zygmund‐type strong law of large numbers is obtained. Our result generalizes the corresponding one of Zhou et al. (2011) and improves the corresponding one of Wang et al. (2011, 2012).

Suggested Citation

  • Aiting Shen, 2013. "On Strong Convergence for Weighted Sums of a Class of Random Variables," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:216236
    DOI: 10.1155/2013/216236
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    References listed on IDEAS

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    1. Sergey Utev & Magda Peligrad, 2003. "Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 16(1), pages 101-115, January.
    2. Soo Sung, 2011. "On the strong convergence for weighted sums of random variables," Statistical Papers, Springer, vol. 52(2), pages 447-454, May.
    3. Wu, Wei Biao, 1999. "On the strong convergence of a weighted sum," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 19-22, August.
    4. Xuejun Wang & Shuhe Hu & Wenzhi Yang & Xinghui Wang, 2012. "On Complete Convergence of Weighted Sums for Arrays of Rowwise Asymptotically Almost Negatively Associated Random Variables," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Qunying Wu, 2012. "Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Guang-hui Cai, 2008. "Strong laws for weighted sums of NA random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 323-331, November.
    7. Qunying Wu, 2012. "Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, July.
    8. Bai, Z. D. & Cheng, Philip E., 2000. "Marcinkiewicz strong laws for linear statistics," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 105-112, January.
    9. Qi-Man Shao, 2000. "A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 13(2), pages 343-356, April.
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