Browse > Article
http://dx.doi.org/10.4134/BKMS.b190391

ON THE CONVERGENCE OF SERIES FOR ROWWISE SUMS OF NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES  

Huang, Haiwu (College of Mathematics and Statistics Hengyang Normal University)
Zhang, Qingxia (School of Sciences Southwest Petroleum University)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.3, 2020 , pp. 607-622 More about this Journal
Abstract
In the paper, some probability convergence properties of series for rowwise sums of negatively superadditive dependent (NSD) random variables are discussed. We establish some sharp results on these convergence for NSD random variables under some general settings, which generalize and improve the corresponding ones of some known literatures.
Keywords
NSD random variables; probability convergence of series;
Citations & Related Records
연도 인용수 순위
  • Reference
1 X. Wang, X. Deng, L. Zheng, and S. Hu, Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications, Statistics 48 (2014), no. 4, 834-850. https://doi.org/10.1080/02331888.2013.800066   DOI
2 X.Wang, A. Shen, Z. Chen, and S. Hu, Complete convergence for weighted sums of NSD random variables and its application in the EV regression model, TEST 24 (2015), no. 1, 166-184. https://doi.org/10.1007/s11749-014-0402-6   DOI
3 K. Joag-Dev and F. Proschan, Negative association of random variables, with applications, Ann. Statist. 11 (1983), no. 1, 286-295. https://doi.org/10.1214/aos/1176346079   DOI
4 J. H. B. Kemperman, On the FKG-inequality for measures on a partially ordered space, Nederl. Akad. Wetensch. Proc. Ser. A 80=Indag. Math. 39 (1977), no. 4, 313-331.   DOI
5 B. Meng, D. Wang, and Q. Wu, Complete convergence and complete moment convergence for arrays of rowwise negatively superadditive dependent random variables, Comm. Statist. Theory Methods 47 (2018), no. 16, 3910-3922. https://doi.org/10.1080/03610926.2017.1364391   DOI
6 H. Naderi, M. Amini, and A. Bozorgnia, On the rate of complete convergence for weighted sums of NSD random variables and an application, Appl. Math. J. Chinese Univ. Ser. B 32 (2017), no. 3, 270-280. https://doi.org/10.1007/s11766-017-3437-0   DOI
7 Y. Shen, X. Wang, W. Yang, and S. Hu, Almost sure convergence theorem and strong stability for weighted sums of NSD random variables, Acta Math. Sin. (Engl. Ser.) 29 (2013), no. 4, 743-756. https://doi.org/10.1007/s10114-012-1723-6   DOI
8 A. Shen, M. Xue, and A. Volodin, Complete moment convergence for arrays of rowwise NSD random variables, Stochastics 88 (2016), no. 4, 606-621. https://doi.org/10.1080/17442508.2015.1110153   DOI
9 A. Shen, Y. Zhang, and A. Volodin, Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables, Metrika 78 (2015), no. 3, 295-311. https://doi.org/10.1007/s00184-014-0503-y   DOI
10 Y. S. Chow, On the rate of moment convergence of sample sums and extremes, Bull. Inst. Math. Acad. Sinica 16 (1988), no. 3, 177-201.
11 T. C. Christofides and E. Vaggelatou, A connection between supermodular ordering and positive/negative association, J. Multivariate Anal. 88 (2004), no. 1, 138-151. https://doi.org/10.1016/S0047-259X(03)00064-2   DOI
12 X. Deng, X. J. Wang, Y. Wu, and Y. Ding, Complete moment convergence and complete convergence for weighted sums of NSD random variables, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 110 (2016), no. 1, 97-120. https://doi.org/10.1007/s13398-015-0225-7   DOI
13 N. Eghbal, M. Amini, and A. Bozorgnia, Some maximal inequalities for quadratic forms of negative superadditive dependence random variables, Statist. Probab. Lett. 80 (2010), no. 7-8, 587-591. https://doi.org/10.1016/j.spl.2009.12.014   DOI
14 N. Eghbal, M. Amini, and A. Bozorgnia, On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables, Statist. Probab. Lett. 81 (2011), no. 8, 1112-1120. https://doi.org/10.1016/j.spl.2011.03.005   DOI
15 Y. Wu and D. Zhu, Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables, J. Korean Statist. Soc. 39 (2010), no. 2, 189-197. https://doi.org/10.1016/j.jkss.2009.05.003   DOI
16 X. Wang, Y. Wu, and S. Hu, Strong and weak consistency of LS estimators in the EV regression model with negatively superadditive-dependent errors, AStA Adv. Stat. Anal. 102 (2018), no. 1, 41-65. https://doi.org/10.1007/s10182-016-0286-8   DOI
17 Y. Wu, On complete moment convergence for arrays of rowwise negatively associated random variables, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 108 (2014), no. 2, 669-681. https://doi.org/10.1007/s13398-013-0133-7   DOI
18 Y. Wu, X. Wang, and S. Hu, Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications, Appl. Math. J. Chinese Univ. Ser. B 31 (2016), no. 4, 439-457. https://doi.org/10.1007/s11766-016-3406-z   DOI
19 P. L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 25-31. https://doi.org/10.1073/pnas.33.2.25   DOI
20 S. Gan and P. Chen, On the limiting behavior of the maximum partial sums for arrays of rowwise NA random variables, Acta Math. Sci. Ser. B (Engl. Ed.) 27 (2007), no. 2, 283-290. https://doi.org/10.1016/S0252-9602(07)60027-7   DOI
21 T.-C. Hu, Negatively superadditive dependence of random variables with applications, Chinese J. Appl. Probab. Statist. 16 (2000), no. 2, 133-144.   DOI
22 T.-C. Hu and R. L. Taylor, On the strong law for arrays and for the bootstrap mean and variance, Internat. J. Math. Math. Sci. 20 (1997), no. 2, 375-382. https://doi.org/10.1155/S0161171297000483   DOI
23 K. Alam and K. M. L. Saxena, Positive dependence in multivariate distributions, Comm. Statist. A-Theory Methods 10 (1981), no. 12, 1183-1196. https://doi.org/10.1080/03610928108828102   DOI