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Meng, Bing; Wang, Dingcheng; Wu, Qunying

Complete convergence and complete moment convergence for arrays of rowwise negatively superadditive dependent random variables. (English) Zbl 1508.60041

Commun. Stat., Theory Methods 47, No. 16, 3910-3922 (2018).
Summary: In this paper, some complete convergence and complete moment convergence results for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are studied. The obtained theorems not only extend the result of S. Gan and P. Chen [Acta Math. Sci., Ser. B, Engl. Ed. 27, No. 2, 283–290 (2007; Zbl 1125.60027)] to the case of NSD random variables, but also improve them.

Cited in 7 Documents

MSC:

60F15 Strong limit theorems

Keywords:

complete convergence; complete moment convergence; negatively superadditive dependent random variables

Citations:

Zbl 1125.60027
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Full Text: DOI

References:

[1] Chow, Y. S. 1988. On the rate of moment convergence of sample sums and extremes. Bulletin of the Institute of Mathematics. Academia Sinica 16 (3):177-201. · Zbl 0655.60028
[2] Christofides, T. C., and E. Vaggelatou. 2004. A connection between supermodular ordering and positive/negative association. Journal of Multivariate Analysis 88:138-51. · Zbl 1034.60016 · doi:10.1016/S0047-259X(03)00064-2
[3] Deng, X., X. J. Wang, and Y. Wu, and Y. Ding. 2016. Complete moment convergence and complete convergence for weighted sums of NSD random variables. RACSAM 110:97-120. · Zbl 1334.60037 · doi:10.1007/s13398-015-0225-7
[4] Eghbal, N., and M. Amini, and A. Bozorgnia. 2010. Some maximal inequalities for quadratic forms of negative superadditive dependence random variables. Statistics & Probability Letters 80:587-91. · Zbl 1187.60020 · doi:10.1016/j.spl.2009.12.014
[5] Gan, S. X., and P. Y. Chen. 2007. On the limiting behavior of the maximum partial sums for arrays of rowwise NA random variables. Acta Mathematica Scientia. Series B 27 (2):283-90. · Zbl 1125.60027 · doi:10.1016/S0252-9602(07)60027-7
[6] Hsu, P. L., and H. Robbins. 1947. Complete convergence and the law of large numbers. Proceedings of the National Academy of Sciences of the United States of America 33 (2):25-31. · Zbl 0030.20101 · doi:10.1073/pnas.33.2.25
[7] Hu, T. Z. 2000. Negatively superadditive dependence of random variables with applications. Chinese Journal of Applied Probability and Statistics 16:133-44. · Zbl 1050.60502
[8] Joag-Dev, K., and F. Proschan. 1983. Negative association of random variables with applications. Annals of Statistics 11 (1):286-95. · Zbl 0508.62041 · doi:10.1214/aos/1176346079
[9] Kemperman, J. H. B. 1977. On the FKG-inequalities for measures on a partially ordered space. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen: Series A 80:313-31. · Zbl 0384.28012 · doi:10.1016/1385-7258(77)90027-0
[10] Shen, Y., and X. J. Wang, and S. H. Hu. 2013. On the strong convergence and some inequalities for negatively superadditive dependent sequences. Journal of Inequalities and Applications 2013:448. · Zbl 1294.60054 · doi:10.1186/1029-242X-2013-448
[11] Shen, Y., X. J. Wang, W. Z. Yang, and S. H. Hu. 2013. Almost sure convergence theorem and strong stability for weighted sums of NSD random variables. Acta Mathematica Sinica, English Series 29 (4):743-56. · Zbl 1263.60025 · doi:10.1007/s10114-012-1723-6
[12] Shen, A. T., Y. Zhang, and A. Volodin. 2015. Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables. Metrika 78:295-311. · Zbl 1333.60022 · doi:10.1007/s00184-014-0503-y
[13] Wang, X. J., X. Deng, and L. L. Zheng, and S. H. Hu. 2014. Complete convergence for arrays of rowwise negatively superadditive dependent random variablesand its applications. Statistics 48:834-50. · Zbl 1319.60063
[14] Wang, X. J., A. T. Shen, Z. Y. Chen, and S. H. Hu. 2015. Complete convergence for weighted sums of NSD random variables and its application in the EV regression model. TEST 24:166-84. · Zbl 1316.60042 · doi:10.1007/s11749-014-0402-6
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