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Strong convergence properties for asymptotically almost negatively associated sequence. (English) Zbl 1257.62066
Summary: By applying the moment inequality for asymptotically almost negatively associated (in short AANA) random sequences and truncation method, we get the three series theorems for AANA random variables. Moreover, a strong convergence property for the partial sums of AANA random sequence is obtained. In addition, we also study the strong convergence property for weighted sums of AANA random sequences.

MSC:
62H20 Measures of association (correlation, canonical correlation, etc.)
60E15 Inequalities; stochastic orderings
62E20 Asymptotic distribution theory in statistics
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[1] H. W. Block, T. H. Savits, and M. Shaked, “Some concepts of negative dependence,” The Annals of Probability, vol. 10, no. 3, pp. 765-772, 1982. · Zbl 0501.62037 · doi:10.1214/aop/1176993784
[2] K. Joag-Dev and F. Proschan, “Negative association of random variables, with applications,” The Annals of Statistics, vol. 11, no. 1, pp. 286-295, 1983. · Zbl 0508.62041 · doi:10.1214/aos/1176346079
[3] P. Matuła, “A note on the almost sure convergence of sums of negatively dependent random variables,” Statistics & Probability Letters, vol. 15, no. 3, pp. 209-213, 1992. · Zbl 0925.60024 · doi:10.1016/0167-7152(92)90191-7
[4] T. K. Chandra and S. Ghosal, “The strong law of large numbers for weighted averages under dependence assumptions,” Journal of Theoretical Probability, vol. 9, no. 3, pp. 797-809, 1996. · Zbl 0857.60021 · doi:10.1007/BF02214087
[5] T. K. Chandra and S. Ghosal, “Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables,” Acta Mathematica Hungarica, vol. 71, no. 4, pp. 327-336, 1996. · Zbl 0853.60032 · doi:10.1007/BF00114421
[6] D. Yuan and J. An, “Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications,” Science in China A, vol. 52, no. 9, pp. 1887-1904, 2009. · Zbl 1184.62099 · doi:10.1007/s11425-009-0154-z
[7] X. Wang, S. Hu, and W. Yang, “Convergence properties for asymptotically almost negatively associated sequence,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 218380, 15 pages, 2010. · Zbl 1207.60025 · doi:10.1155/2010/218380 · eudml:223503
[8] X. Wang, S. Hu, and W. Yang, “Complete convergence for arrays of rowwise asymptotically almost negatively associated random variables,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 717126, 11 pages, 2011. · Zbl 1235.60026 · doi:10.1155/2011/717126
[9] Y. Wang, J. Yan, F. Cheng, and C. Su, “The strong law of large numbers and the law of the iterated logarithm for product sums of NA and AANA random variables,” Southeast Asian Bulletin of Mathematics, vol. 27, no. 2, pp. 369-384, 2003. · Zbl 1061.60031
[10] J. Baek II, “Almost sure convergence for asymptotically almost negatively associated random variables sequence,” Communications of the Korean Statistical Society, vol. 16, no. 6, pp. 1013-1022, 2009. · doi:10.5351/CKSS.2009.16.6.1013
[11] Q. Y. Wu, “Probability limit theory for mixing sequence,” Sciences Press, 2005 (Chinese).
[12] S. H. Sung, “Strong laws for weighted sums of i.i.d. random variables. II,” Bulletin of the Korean Mathematical Society, vol. 39, no. 4, pp. 607-615, 2002. · Zbl 1027.60028 · doi:10.4134/BKMS.2002.39.4.607
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