Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Almost Sure Convergence for Asymptotically Almost Negatively Associated Random Variable Sequences

  • Baek, Jong-Il (School of Mathematics & Informational Statistics, Wonkwang University)
  • Received : 20090900
  • Accepted : 20091000
  • Published : 2009.11.30
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Abstract

We in this paper study the almost sure convergence for asymptotically almost negatively associated(AANA) random variable sequences and obtain some new results which extend and improve the result of Jamison et al. (1965) and Marcinkiewicz-Zygumnd strong law types in the form given by Baum and Katz (1965), three-series theorem.

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References

  1. Baum, E. and Katz, M. (1965). Convergence rates in the law of large numbers, Transactions of the American Mathematical Society, 120, 108–123
  2. Chandra, T. K. and Ghosal, S. (1996a). Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables, Acta Mathematica Hungarica, 71, 327–336 https://doi.org/10.1007/BF00114421
  3. Chandra, T. K. and Ghosal, S. (1996b). The strong law of large numbers for weighted averages under dependence assumption, Journal of Theoretical Probability, 9, 797–809 https://doi.org/10.1007/BF02214087
  4. Jamison, B., Orey, S. and Pruitt,W. (1965). Convergence of weighted averages of independent random variables, Probability Theory and Related Fields, 4, 40–44 https://doi.org/10.1007/BF00535481
  5. Joag-Dev, K. and Proschan, F. (1983). Negative association of random variables with applications, The Annals of Statistics, 11, 286–295
  6. Stout W. F. (1974). Almost Sure Convergence, Academic Press, New York

Cited by

  1. Strong Convergence Properties for Asymptotically Almost Negatively Associated Sequence vol.2012, 2012, https://doi.org/10.1155/2012/562838