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http://dx.doi.org/10.4134/BKMS.b180791

COMPLETE CONVERGENCE AND COMPLETE MOMENT CONVERGENCE THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF ROWWISE EXTENDED NEGATIVELY 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.56, no.4, 2019 , pp. 1007-1025 More about this Journal
Abstract
In the present work, the complete convergence and complete moment convergence properties for arrays of rowwise extended negatively dependent (END) random variables are investigated. Some sharp theorems on these strong convergence for weighted sums of END cases are established. These main results not only generalize the known corresponding ones of Cai [2], Wang et al. [17] and Shen [14], but also improve them, respectively.
Keywords
arrays of rowwise END random variables; complete convergence; complete moment convergence; weighted sums;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 N. Asadian, V. Fakoor, and A. Bozorgnia, Rosental's type inequalities for negatively orthant dependent random variables, J. Iranian Stat. Soc. 5 (2006), no. 1-2, 66-75.
2 G. Cai, Strong laws for weighted sums of NA random variables, Metrika 68 (2008), no. 3, 323-331. https://doi.org/10.1007/s00184-007-0160-5   DOI
3 Y. Chen, A. Chen, and K. W. Ng, The strong law of large numbers for extended negatively dependent random variables, J. Appl. Probab. 47 (2010), no. 4, 908-922. https://doi.org/10.1239/jap/1294170508   DOI
4 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.
5 N. Ebrahimi and M. Ghosh, Multivariate negative dependence, Comm. Statist. A-Theory Methods 10 (1981), no. 4, 307-337.   DOI
6 T.-C. Hu, A. Rosalsky, and K.-L. Wang, Complete convergence theorems for extended negatively dependent random variables, Sankhya A 77 (2015), no. 1, 1-29. https://doi.org/10.1007/s13171-014-0058-z   DOI
7 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
8 C. Liu, M. Guo, and D. Zhu, Equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables, Commun. Math. Res. 31 (2015), no. 1, 40-50.
9 L. Liu, Precise large deviations for dependent random variables with heavy tails, Statist. Probab. Lett. 79 (2009), no. 9, 1290-1298. https://doi.org/10.1016/j.spl.2009.02.001   DOI
10 L. Liu, Necessary and suffcient conditions for moderate deviations of dependent random variables with heavy tails, Sci. China Math. 53 (2010), no. 6, 1421-1434. https://doi.org/10.1007/s11425-010-4012-9   DOI
11 D. H. Qiu, P. Y. Chen, R. G. Antonini, and A. Volodin. On the complete convergence for arrays of rowwise extended negatively dependent random variables, J. Korean Math. Soc. 50 (2013), no. 2, 379-392. https://doi.org/10.4134/JKMS.2013.50.2.379   DOI
12 A. Shen, Probability inequalities for END sequence and their applications, J. Inequal. Appl. 2011 (2011), 98, 12 pp. https://doi.org/10.1186/1029-242X-2011-98   DOI
13 E. L. Lehmann, Some concepts of dependence, Ann. Math. Statist. 37 (1966), 1137-1153. https://doi.org/10.1214/aoms/1177699260   DOI
14 A. Shen, On the strong convergence rate for weighted sums of arrays of rowwise negatively orthant dependent random variables, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 107 (2013), no. 2, 257-271. https://doi.org/10.1007/s13398-012-0067-5   DOI
15 A. Shen and R. Wu, Strong convergence results for weighted sums of $\tilde-\rho}$-mixing random variables, J. Inequal. Appl. 2013 (2013), 327, 11 pp. https://doi.org/10.1186/1029-242X-2013-327   DOI
16 X. Wang, T. C. Hu, A. Volodin, and S. H. Hu, Complete convergence for weighted sums and arrays of rowwise extended negatively dependent random variables, Comm. Statist. Theory Methods 42 (2013), no. 13, 2391-2401. https://doi.org/10.1080/03610926.2011.609321   DOI
17 S. Wang and X. Wang, Precise large deviations for random sums of END real-valued random variables with consistent variation, J. Math. Anal. Appl. 402 (2013), no. 2, 660-667. https://doi.org/10.1016/j.jmaa.2013.02.002   DOI
18 X. Wang, S. Hu, and W. Yang, Complete convergence for arrays of rowwise negatively orthant dependent random variables, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 106 (2012), no. 2, 235-245. https://doi.org/10.1007/s13398-011-0048-0   DOI
19 X. Wang, X. Q. Li, S. H. Hu, and X. H. Wang, On complete convergence for an extended negatively dependent sequence, Comm. Statist. Theory Methods 43 (2014), no. 14, 2923-2937. https://doi.org/10.1080/03610926.2012.690489   DOI
20 S.Wang and W.Wang, Extended precise large deviations of random sums in the presence of END structure and consistent variation, J. Appl. Math. 2012 (2012), Art. ID 436531, 12 pp. https://doi.org/10.1155/2012/436531   DOI
21 Q. Wu, Complete convergence for weighted sums of sequences of negatively dependent random variables, J. Probab. Stat. 2011 (2011), Art. ID 202015, 16 pp. https://doi.org/10.1155/2011/202015   DOI
22 X. Wang, S. J. Wang, S. H. Hu, J. Ling, and Y. Wei, On complete convergence of weighted sums for arrays of rowwise extended negatively dependent random variables, Stochastics 85 (2013), no. 6, 1060-1072. https://doi.org/10.1080/17442508.2012.736996   DOI
23 X. Wang, L. L. Zheng, C. Xu, and S. H. Hu, Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors, Statistics 49 (2015), no. 2, 396-407. https://doi.org/10.1080/02331888.2014.888431   DOI
24 Q. Wu. Probability Limit Theory for Mixing and Dependent Sequences, Science Press of China, Beijing, 2006.
25 Y. Wu, M. Ordonez Cabrera, and A. Volodin, Complete convergence and complete moment convergence for arrays of rowwise end random variables, Glas. Mat. Ser. III 49(69) (2014), no. 2, 447-466. https://doi.org/10.3336/gm.49.2.16
26 Y. Wu, S. H. Sung, and A. Volodin, A note on the rates of convergence for weighted sums of ${\rho}*$-mixing random variables, Lith. Math. J. 54 (2014), no. 2, 220-228. https://doi.org/10.1007/s10986-014-9239-7   DOI
27 Y. Wu and M. Guan, Convergence properties of the partial sums for sequences of end random variables, J. Korean Math. Soc. 49 (2012), no. 6, 1097-1110. https://doi.org/10.4134/JKMS.2012.49.6.1097   DOI