Title:
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Strong Convergence for weighed sums of negatively superadditive dependent random variables (English) |
Author:
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Chen, Zhiyong |
Author:
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Wang, Haibin |
Author:
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Wang, Xuejun |
Author:
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Hu, Shuhe |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 (print) |
ISSN:
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1805-949X (online) |
Volume:
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52 |
Issue:
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1 |
Year:
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2016 |
Pages:
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52-65 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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In this paper, the strong law of large numbers for weighted sums of negatively superadditive dependent (NSD, in short) random variables is obtained, which generalizes and improves the corresponding one of Bai and Cheng ([2]) for independent and identically distributed random variables to the case of NSD random variables. (English) |
Keyword:
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NSD random variables |
Keyword:
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weighted sums |
Keyword:
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strong law of large numbers |
MSC:
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60F15 |
idZBL:
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Zbl 06562212 |
idMR:
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MR3482610 |
DOI:
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10.14736/kyb-2016-1-0052 |
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Date available:
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2016-03-21T17:50:59Z |
Last updated:
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2018-01-10 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/144862 |
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Reference:
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[1] Alam, K., Saxena, K. M. L.: Positive dependence in multivariate distributions..Commun. Statist. - Theory and Methods 10 (1981), 12, 1183-1196. Zbl 0471.62045, MR 0623526, 10.1080/03610928108828102 |
Reference:
|
[2] Bai, Z. D., Cheng, P. E.: Marcinkiewicz strong laws for linear statistics..Statist. Probab. Lett. 46 (2000), 2, 105-112. Zbl 0960.60026, MR 1748864, 10.1016/s0167-7152(99)00093-0 |
Reference:
|
[3] Block, H. M., Savits, T. H., Shaked, M.: Some concepts of negative dependence..Ann. Probab. 10 (1982), 3, 765-772. Zbl 0501.62037, MR 0659545, 10.1214/aop/1176993784 |
Reference:
|
[4] Budsaba, K., Chen, P., Panishkan, K., Volodin, A.: Strong laws for weighted sums and certain types U-statistics based on negatively associated random variables..Siberian Advances in Mathematics 19 (2009), 4, 225-232. MR 2655933, 10.3103/s1055134409040014 |
Reference:
|
[5] Christofides, T. C., Vaggelatou, E.: A connection between supermodular ordering and positive/negative association..J. Multivariate Anal. 88 (2004), 1, 138-151. Zbl 1034.60016, MR 2021866, 10.1016/s0047-259x(03)00064-2 |
Reference:
|
[6] Eghbal, N., Amini, M., Bozorgnia, A.: Some maximal inequalities for quadratic forms of negative superadditive dependence random variables..Statist. Probab. Lett. 80 (2010), 7, 587-591. Zbl 1187.60020, MR 2595134, 10.1016/j.spl.2009.12.014 |
Reference:
|
[7] Eghbal, N., Amini, M., Bozorgnia, A.: On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables..Statist. Probab. Lett. 81 (2011), 8, 1112-1120. Zbl 1228.60039, MR 2803752, 10.1016/j.spl.2011.03.005 |
Reference:
|
[8] Gerasimov, M., Kruglov, V., Volodin, A.: On negatively associated random variables..Lobachevskii J. Math. 33 (2012), 1, 47-55. Zbl 1255.60029, MR 2910806, 10.1134/s1995080212010052 |
Reference:
|
[9] Hu, S. H., Liu, X. T., Wang, X. H., Li, X. T.: Strong law of large numbers of partial sums for pairwise NQD sequences..J. Math. Res. Appl. 33 (2013), 1, 111-116. Zbl 1289.60039, MR 3077034 |
Reference:
|
[10] Hu, T. Z.: Negatively superadditive dependence of random variables with applications..Chinese J. App. Probab. Statist. 16 (2000), 133-144. Zbl 1050.60502, MR 1812714 |
Reference:
|
[11] Joag-Dev, K., Proschan, F.: Negative association ofrandom variables with applications..Ann. Statist. 11 (1983), 1, 286-295. MR 0684886, 10.1214/aos/1176346079 |
Reference:
|
[12] Jing, B. Y., Liang, H. Y.: Strong limit theorems for weighted sums of negatively associated random variables..J. Theoret. Probab. 21 (2008), 4, 890-909. Zbl 1162.60008, MR 2443640, 10.1007/s10959-007-0128-4 |
Reference:
|
[13] Matula, P.: A note on the almost sure convergence of sums of negatively dependent random variables..Statistics and Probability Letters, 15 (1992), 209-213. Zbl 0925.60024, MR 1190256, 10.1016/0167-7152(92)90191-7 |
Reference:
|
[14] Meng, Y. J., Lin, Z. Y.: Strong laws of large numbers for $\tilde{\rho}$-mixing random variables..J. Math. Anal. Appl. 365 (2010), 711-717. Zbl 1186.60028, MR 2587074, 10.1016/j.jmaa.2009.12.009 |
Reference:
|
[15] Shao, Q. M.: A comparison theorem on moment inequalities between negatively associated and independent random variables..J. Theoret. Probab. 13 (2000), 2, 343-356. Zbl 0971.60015, MR 1777538, 10.1023/A:1007849609234 |
Reference:
|
[16] Shen, A. T., Wu, R. C.: Strong and weak convergence for asymptotically almost negatively associated random variables..Discrete Dynamics in Nature and Society 2013 (2013), 1-7. Zbl 1269.60036, MR 3037709, 10.1155/2013/235012 |
Reference:
|
[17] 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:
|
[18] Shen, A. T.: On strong convergence for weighted sums of a class of random variables..Abstract Appl. Anal. 2013 (2013), 1-7. Zbl 1279.60041, MR 3035392, 10.1155/2013/216236 |
Reference:
|
[19] Shen, A. T., Zhang, Y., Volodin, A.: Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables..Metrika 78 (2015), 295-311. MR 3320899, 10.1007/s00184-014-0503-y |
Reference:
|
[20] Shen, Y., Wang, X. J., Yang, W. Z., Hu, S. H.: Almost sure convergence theorem and strong stability for weighted sums of NSD random variables..Acta Mathematica Sinica, English Series, 29 (2013), 4, 743-756. Zbl 1263.60025, MR 3029287, 10.1007/s10114-012-1723-6 |
Reference:
|
[21] Shen, Y., Wang, X. J., Hu, S. H.: On the strong convergence and some inequalities for negatively superadditive dependent sequences..J. Inequalities Appl. 2013 (2013), 1, 448. Zbl 1294.60054, MR 3339510, 10.1186/1029-242x-2013-448 |
Reference:
|
[22] Sung, S. H.: On the strong law of large numbers for weighted sums of random variables..Computers Math. Appl. 62 (11) (2011), 4277-4287. Zbl 1238.60040, MR 2859983, 10.1016/j.camwa.2011.10.018 |
Reference:
|
[23] Wang, X. J., Li, X. Q., Hu, S. H., Yang, W. Z.: Strong limit theorems for weighted sums of negatively associated random variables..Stochast. Anal. Appl. 29 (2011), 1, 1-14. Zbl 1208.60028, MR 2763547, 10.1080/07362994.2010.515484 |
Reference:
|
[24] 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:
|
[25] Wang, X.J., Deng, X., Zheng, L.L., Hu, S.H.: Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications..Statistics 48 (4) (2014), 834-850. Zbl 1319.60063, MR 3234065, 10.1080/02331888.2013.800066 |
Reference:
|
[26] Wang, X. J., Shen, A. T., Chen, Z. Y., Hu, S. H.: Complete convergence for weighted sums of NSD random variables and its application in the EV regression model..Test 24 (2015), 166-184. Zbl 1316.60042, MR 3314578, 10.1007/s11749-014-0402-6 |
Reference:
|
[27] Wu, Q. Y.: Probability Limit Theory for Mixing Sequence..Science Press of China, Beijing 2006. |
Reference:
|
[28] Wu, Q. Y., Jiang, Y. Y.: A law of the iterated logarithm of partial sums for NA random variables..J. Korean Statist. Soc. 39 (2010), 199-206. Zbl 1294.60055, MR 2642486, 10.1016/j.jkss.2009.06.001 |
Reference:
|
[29] Wu, Q. Y., Jiang, Y. Y.: Chover's law of the iterated logarithm for negatively associated sequences..J. Systems Sci. Complex. 23 (2010), 293-302. Zbl 1205.60069, MR 2653591, 10.1007/s11424-010-7258-y |
Reference:
|
[30] Yang, W. Z, Hu, S. H., Wang, X. J., Zhang, Q. C.: Berry-Esséen bound of sample quantiles for negatively associated sequence..J. Inequalities Appl. 2011 (2011), 1, 83. MR 2847593, 10.1186/1029-242x-2011-83 |
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