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Asymptotics for a class of dependent random variables

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  • Zhang, Li-Xin
  • Zhang, Yang

Abstract

We consider a class of dependent random variables where the dependence structure involves a factor driven by Sn/n. Under very mild conditions for the innovation, we obtain several asymptotic results for the partial sums including basic asymptotics and strong limit theorems. The fact that the asymptotic properties differ strikingly in a neighbour of a critical point makes the model very interesting.

Suggested Citation

  • Zhang, Li-Xin & Zhang, Yang, 2015. "Asymptotics for a class of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 47-56.
    • Handle: RePEc:eee:stapro:v:105:y:2015:i:c:p:47-56
    DOI: 10.1016/j.spl.2015.05.018
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    References listed on IDEAS

    as
    1. Peligrad, Magda & Sang, Hailin, 2012. "Asymptotic Properties Of Self-Normalized Linear Processes With Long Memory," Econometric Theory, Cambridge University Press, vol. 28(3), pages 548-569, June.
    2. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas & Koul, Hira L., 2014. "Asymptotic Normality For Weighted Sums Of Linear Processes," Econometric Theory, Cambridge University Press, vol. 30(1), pages 252-284, February.
    3. repec:bla:anzsta:v:46:y:2004:i:1:p:53-57 is not listed on IDEAS
    4. James, Barry & James, Kang & Qi, Yongcheng, 2008. "Limit theorems for correlated Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2339-2345, October.
    5. Wu, Lan & Qi, Yongcheng & Yang, Jingping, 2012. "Asymptotics for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 455-463.
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