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Maximal inequalities and laws of large numbers for Lq-mixingale arrays

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  • Meng, Yanjiao
  • Lin, Zhengyan

Abstract

In this paper we obtain two inequalities of the maximum of partial sums of an Lq-mixingale array, and as corollary a strong law of large numbers (SLLN) for an Lq-mixingale sequence is shown by using the moment inequality. Finally, we prove a weak law of large numbers (WLLN) for an Lq-mixingale array without the condition of uniform integrability which is needed in Andrews [Andrews, D.W.K., 1988. Laws of large numbers for dependent non-identically distributed random variables. Econometric Theory 4, 458-467].

Suggested Citation

  • Meng, Yanjiao & Lin, Zhengyan, 2009. "Maximal inequalities and laws of large numbers for Lq-mixingale arrays," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1539-1547, July.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:13:p:1539-1547
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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. Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(2), pages 213-221, June.
    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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