Previous |  Up |  Next

Article

Title: Convergence of the tail probability for weighted sums of negatively orthant dependent random variables (English)
Author: Huang, Haiwu
Author: Li, Linyan
Author: Lu, Xuewen
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 56
Issue: 4
Year: 2020
Pages: 646-661
Summary lang: English
.
Category: math
.
Summary: In this research, strong convergence properties of the tail probability for weighted sums of negatively orthant dependent random variables are discussed. Some sharp theorems for weighted sums of arrays of rowwise negatively orthant dependent random variables are established. These results not only extend the corresponding ones of Cai [4], Wang et al. [19] and Shen [13], but also improve them, respectively. (English)
Keyword: negatively orthant dependent random variables
Keyword: the tail probability
Keyword: strong convergence
MSC: 60F15
MSC: 62G32
idZBL: Zbl 07286040
idMR: MR4168529
DOI: 10.14736/kyb-2020-4-0646
.
Date available: 2020-10-30T16:22:05Z
Last updated: 2021-02-23
Stable URL: http://hdl.handle.net/10338.dmlcz/148377
.
Reference: [1] Amini, M., Bozorgnia, A.: Complete convergence for negatively dependent random variables..J. Appl. Math. Stoch. Anal. 16 (2003), 121-126. MR 1989578, 10.1155/s104895330300008x
Reference: [2] Asadian, N., Fakoor, V., Bozorgnia, A.: Rosental's type inequalities for negatively orthant dependent random variables..J. Iranian Stat. Soc. 5 (2006), 1-2, 66-75.
Reference: [3] Bozorgnia, A., Patterson, R. F., Taylor, R. L.: Limit theorems for dependent random variables.World Congress Nonlinear Analysts'92 (1996), pp. 1639-1650. MR 1389197, 10.1515/9783110883237.1639
Reference: [4] Cai, G. H.: Strong laws for weighted sums of NA random variables..Metrika 68 (2008), 323-331. Zbl 1247.60036, MR 2448963, 10.1007/s00184-007-0160-5
Reference: [5] Chow, Y. S.: On the rate of moment complete convergence of sample sums and extremes..Bull. Inst. Math. Acad. Sinica 16 (1988), 177-201. MR 1089491
Reference: [6] Ebrahimi, N., Ghosh, M.: Multivariate negative dependence..Commun. Stat., Theory Methods 10 (1981), 307-337. MR 0612400, 10.1080/03610928108828041
Reference: [7] Gan, S. X., Chen, P. Y.: Some limit theorems for weighted sums of arrays of NOD random variables..Acta. Math. Sci.32B (2012), 6, 2388-2400. MR 2989424, 10.1016/s0252-9602(12)60187-8
Reference: [8] Huang, H. W., Wang, D. C.: A note on the strong limit theorem for weighted sums of sequences of negatively dependent random variables..J. Inequal. Appl. (2012). Zbl 1280.60022, MR 2678912, 10.1186/1029-242x-2012-233
Reference: [9] Joag-Dev, K., Proschan, F.: Negative association of random variables with applications..Ann. Stat. 11 (1983), 1, 286-295. MR 0684886, 10.1214/aos/1176346079
Reference: [10] Kuczmaszewska, A.: On some conditions for complete convergence for arrays of rowwise negatively dependent random variables..Stoch. Anal. Appl. 24 (2006), 1083-1095. MR 2273771, 10.1080/07362990600958754
Reference: [11] Qiu, D. H., Liu, X. D., Chen, P. Y.: Complete moment convergence for maximal partial sums under NOD setup..J. Inequal. Appl. 2015. MR 3313861, 10.1186/s13660-015-0577-8
Reference: [12] Qiu, D. H., Wu, Q. Y., Chen, P. Y.: Complete convergence for negatively orthant dependent random variables..J. Inequal. Appl. (2014). MR 3255876, 10.1186/1029-242x-2014-145
Reference: [13] Shen, A. T.: On the strong convergence rate for weighted sums of arrays of rowwise negatively orthant dependent random variables..RACSAM 107 (2013), 2, 257-271. Zbl 1278.60060, MR 3199709, 10.1007/s13398-012-0067-5
Reference: [14] Shen, A. T., Wu, R. C.: Strong convergence results for weighted sums of $\tilde{\rho }$-mixing random variables..J. Inequal. Appl. (2013). Zbl 1287.60040, MR 3081708, 10.1186/1029-242x-2013-327
Reference: [15] Sung, S. H.: On the exponential inequalities for negatively dependent random variables..J. Math. Anal. Appl. 381 (2011), 538-545. MR 2802091, 10.1016/j.jmaa.2011.02.058
Reference: [16] Volodin, A.: On the Kolmogorov exponential inequality for negatively dependent random variables..Pakistan J. Stat. 18 (2002), 249-254. MR 1944611
Reference: [17] Wang, X. J., Hu, S. H., Shen, A. T., Yang, W. Z.: An exponential inequality for a NOD sequence and a strong law of large numbers.Appl. Math. Lett. 24 (2011), 219-223. MR 2735145, 10.1016/j.aml.2010.09.007
Reference: [18] Wang, X. J., Hu, S. H., Volodin, A.: Strong limit theorems for weighted sums of NOD sequence and exponential inequalities..Bull. Korean Math. Soc.48 (2011), 5, 923-938. MR 2867181, 10.4134/bkms.2011.48.5.923
Reference: [19] Wang, X. J., Hu, S. H., Yang, W. Z.: Complete convergence for arrays of rowwise negatively orthant dependent random variables..RACSAM 106 (2012), 2, 235-245. Zbl 1260.60062, MR 2978912, 10.1007/s13398-011-0048-0
Reference: [20] Wu, Q. Y.: Complete convergence for negatively dependent sequences of random variables..J. Inequal. Appl. (2010), Article ID 507293. Zbl 1202.60050, MR 2611036, 10.1155/2010/507293
Reference: [21] Wu, Q. Y.: Complete convergence for weighted sums of sequences of negatively dependent random variables..J. Probab. Stat. (2011), Article ID 202015. MR 2774947, 10.1155/2011/202015
Reference: [22] Wu, Q. Y.: Probability Limit Theory for Mixing and Dependent Sequences..Science Press of China, Beijing 2006.
Reference: [23] Wu, Y. F., Sung, S. H., Volodin, A.: A note on the rates of convergence for weighted sums of ${\rho^*}$-mixing random variables..Lith. Math. J. 54 (2014), 2, 220-228. MR 3212638, 10.1007/s10986-014-9239-7
Reference: [24] Wu, Y. F., Zhu, D. J.: Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables..J. Korean Stat. Soc. 39 (2010), 189-197. MR 2642485, 10.1016/j.jkss.2009.05.003
Reference: [25] Zarei, H., Jabbari, H.: Complete convergence of weighted sums under negative dependence..Stat. Pap. 52 (2009), 413-418. MR 2795888, 10.1007/s00362-009-0238-4
Reference: [26] Zhang, Q. X., Wang, D. C.: A note on the rate of strong convergence for weighted sums of arrays of rowwise negatively orthant dependent random variables..Discrete Dyn. Nat. Soc. (2014), Article ID 368702. MR 3253602, 10.1155/2014/368702
.

Files

Files Size Format View
Kybernetika_56-2020-4_3.pdf 489.5Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo