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On the weak laws of large numbers for arrays of random variables

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  • Meng, Yanjiao
  • Lin, Zhengyan

Abstract

In this paper we obtain weak laws of large numbers (WLLNs) for arrays of random variables under the uniform Cesàro-type condition. As corollary, we obtain the result of Hong and Oh [Hong, D. H., Oh, K. S., 1995. On the weak law of large numbers for arrays. Statist. Probab. Lett. 22, 55-57]. Furthermore, we obtain a WLLN for an Lp-mixingale array without the conditions that the mixingale is uniformly integrable and the Lp-mixingale numbers decay to zero at a special rate.

Suggested Citation

  • Meng, Yanjiao & Lin, Zhengyan, 2009. "On the weak laws of large numbers for arrays of random variables," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2405-2414, December.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:23:p:2405-2414
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    References listed on IDEAS

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    1. Li, Yulin, 2003. "A martingale inequality and large deviations," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 317-321, April.
    2. Dug Hun Hong & Kwang Sik Oh, 1995. "On the weak law of large numbers for arrays," Statistics & Probability Letters, Elsevier, vol. 22(1), pages 55-57, January.
    3. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
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