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Complete convergence for weighted sums of sequences of negatively dependent random variables. (English) Zbl 1221.60041
Summary: The application of the complete convergence for weighted sums of sequences of negatively dependent random variables to the moment inequality of negatively dependent random variables is discussed. As a result, complete convergence theorems for negatively dependent sequences of random variables are extended.

MSC:
60F15Strong limit theorems
WorldCat.org
Full Text: DOI EuDML
References:
[1] E. L. Lehmann, “Some concepts of dependence,” Annals of Mathematical Statistics, vol. 37, no. 5, pp. 1137-1153, 1966. · Zbl 0146.40601 · doi:10.1214/aoms/1177699260
[2] A. Bozorgnia, R. F. Patterson, and R. L. Taylor, “Limit theorems for ND r.v.’s,” Tech. Rep., University of Georgia, Athens, Ga, USA, 1993.
[3] 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
[4] M. Amini, Some contribution to limit theorems for negatively dependent random variable, Ph.D. thesis, 2000.
[5] V. Fakoor and H. A. Azarnoosh, “Probability inequalities for sums of negatively dependent random variables,” Pakistan Journal of Statistics, vol. 21, no. 3, pp. 257-264, 2005. · Zbl 1129.60303
[6] H. R. Nili Sani, M. Amini, and A. Bozorgnia, “Strong laws for weighted sums of negative dependent random variables,” Islamic Republic of Iran. Journal of Sciences, vol. 16, no. 3, pp. 261-265, 2005.
[7] O. Klesov, A. Rosalsky, and A. I. Volodin, “On the almost sure growth rate of sums of lower negatively dependent nonnegative random variables,” Statistics & Probability Letters, vol. 71, no. 2, pp. 193-202, 2005. · Zbl 1070.60030 · doi:10.1016/j.spl.2004.10.027
[8] Q. Y. Wu and Y. Y. Jiang, “The strong consistency of M estimator in a linear model for negatively dependent random samples,” Communications in Statistics, vol. 40, no. 3, pp. 467-491, 2011. · Zbl 1208.62039 · doi:10.1080/03610920903427792
[9] H. P. Rosenthal, “On the subspaces of Lp(P>2) spanned by sequences of independent random variables,” Israel Journal of Mathematics, vol. 8, pp. 273-303, 1970. · Zbl 0213.19303 · doi:10.1007/BF02771562
[10] W. F. Stout, Almost Sure Convergence, Academic Press, New York, NY, USA, 1974. · Zbl 0321.60022
[11] P. L. Hsu and H. Robbins, “Complete convergence and the law of large numbers,” Proceedings of the National Academy of Sciences of the United States of America, vol. 33, pp. 25-31, 1947. · Zbl 0030.20101 · doi:10.1073/pnas.33.2.25
[12] L. E. Baum and M. Katz, “Convergence rates in the law of large numbers,” Transactions of the American Mathematical Society, vol. 120, pp. 108-123, 1965. · Zbl 0142.14802 · doi:10.2307/1994170
[13] D. L. Li, M. B. Rao, T. F. Jiang, and X. C. Wang, “Complete convergence and almost sure convergence of weighted sums of random variables,” Journal of Theoretical Probability, vol. 8, no. 1, pp. 49-76, 1995. · Zbl 0814.60026 · doi:10.1007/BF02213454
[14] H.-Y. Liang and C. Su, “Complete convergence for weighted sums of NA sequences,” Statistics & Probability Letters, vol. 45, no. 1, pp. 85-95, 1999. · Zbl 0967.60032 · doi:10.1016/S0167-7152(99)00046-2
[15] Q. Y. Wu, “Convergence properties of pairwise NQD random sequences,” Acta Mathematica Sinica. Chinese Series, vol. 45, no. 3, pp. 617-624, 2002 (Chinese). · Zbl 1008.60039
[16] Q. Y. Wu, “Complete convergence for negatively dependent sequences of random variables,” Journal of Inequalities and Applications, vol. 2010, Article ID 507293, 10 pages, 2010. · Zbl 1202.60050 · doi:10.1155/2010/507293 · eudml:225255
[17] S. H. Sung, “Moment inequalities and complete moment convergence,” Journal of Inequalities and Applications, vol. 2009, Article ID 271265, 14 pages, 2009. · Zbl 1180.60019 · doi:10.1155/2009/271265 · eudml:117788