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A general method to the strong law of large numbers and its applications

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  • Yang, Shanchao
  • Su, Chun
  • Yu, Keming

Abstract

A general method to prove the strong law of large numbers is given by using the maximal tail probability. As a result the convergence rate of Sn/n for both positively associated sequences and negatively associated sequences is for any [delta]>1. This result closes to the optimal achievable convergence rate under independent random variables, and improves the rates n-1/3(logn)2/3 and n-1/3(logn)5/3 obtained by Ioannides and Roussas [1999. Exponential inequality for associated random variables. Statist. Probab. Lett. 42, 423-431] and Oliveira [2005. An exponential inequality for associated variables. Statist. Probab. Lett. 73, 189-197], respectively. In this sense the proposed general method may be more effective than its peers provided by Fazekas and Klesov [2001. A general approach to the strong law of large numbers. Theory Probab. Appl. 45(3), 436-449] and Ioannides and Roussas [1999. Exponential inequality for associated random variables. Statist. Probab. Lett. 42, 423-431].

Suggested Citation

  • Yang, Shanchao & Su, Chun & Yu, Keming, 2008. "A general method to the strong law of large numbers and its applications," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 794-803, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:794-803
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    References listed on IDEAS

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    1. Kuczmaszewska, Anna, 2005. "The strong law of large numbers for dependent random variables," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 305-314, July.
    2. Ioannides, D. A. & Roussas, G. G., 1999. "Exponential inequality for associated random variables," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 423-431, May.
    3. Oliveira, Paulo Eduardo, 2005. "An exponential inequality for associated variables," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 189-197, June.
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