Title:
|
Further study on complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated random variables (English) |
Author:
|
Huang, Haiwu |
Author:
|
Zhang, Hanjun |
Author:
|
Zhang, Qingxia |
Author:
|
Peng, Jiangyan |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 (print) |
ISSN:
|
1805-949X (online) |
Volume:
|
51 |
Issue:
|
6 |
Year:
|
2015 |
Pages:
|
960-972 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
In this paper, the authors further studied the complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated (AANA) random variables with non-identical distribution under some mild moment conditions. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of AANA random variables is obtained. The results not only generalize the corresponding ones of Wang et al. [19], but also partially improve the corresponding ones of Huang et al. [8]. (English) |
Keyword:
|
arrays of rowwise AANA random variables |
Keyword:
|
complete convergence |
Keyword:
|
Marcinkiewicz–Zygmund type strong law of large numbers |
Keyword:
|
weighted sums |
MSC:
|
60F15 |
idZBL:
|
Zbl 06537790 |
idMR:
|
MR3453680 |
DOI:
|
10.14736/kyb-2015-6-0960 |
. |
Date available:
|
2016-01-21T18:19:31Z |
Last updated:
|
2018-01-10 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144819 |
. |
Reference:
|
[1] Adler, A., Rosalsky, A.: Some general strong laws for weighted sums of stochastically dominated random variables..Stochastic Anal. Appl. 5 (1987), 1-16. Zbl 0617.60028, MR 0882694, 10.1080/07362998708809104 |
Reference:
|
[2] Adler, A., Rosalsky, A., Taylor, R. L.: Strong laws of large numbers for weighted sums of random variables in normed linear spaces..Int. J. Math. Math. Sci. 12 (1989), 507-530. MR 1007204, 10.1155/s0161171289000657 |
Reference:
|
[3] Bai, Z. D., Cheng, P. E.: Marcinkiewicz strong laws for linear statistics..Stat. Probab. Lett., 46(2) (2000), 105-112. Zbl 0960.60026, MR 1748864, 10.1016/s0167-7152(99)00093-0 |
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] Chandra, T. K., Ghosal, S.: Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables..Acta Math. Hung. 71 (1996), 4, 327-336. Zbl 0853.60032, MR 1397560, 10.1007/bf00114421 |
Reference:
|
[6] Chandra, T. K., Ghosal, S.: The strong law of large numbers for weighted averages under dependence assumptions..J. Theor. Probab. 9 (1996), 3, 797-809. Zbl 0857.60021, MR 1400599, 10.1007/bf02214087 |
Reference:
|
[7] Hu, X. P., Fang, G. H., Zhu, D. J.: Strong convergence properties for asymptotically almost negatively associated sequence..Discrete Dyn. Nat. Soc. 2012 (2012), 1-8. Zbl 1257.62066, MR 2993321, 10.1155/2012/562838 |
Reference:
|
[8] Huang, H. W., Deng, G. M., Zhang, Q. X., Jiang, Y. Y.: On the strong convergence for weighted sums of asymptotically almost negatively associated random variables..Kybernetika 50 (2014), 3, 393-407. Zbl 1301.60030, MR 3245537, 10.14736/kyb-2014-3-0393 |
Reference:
|
[9] 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 (2012), 1, 233. Zbl 1280.60022, MR 3017300, 10.1186/1029-242x-2012-233 |
Reference:
|
[10] Jing, B. Y., Liang, H. Y.: Strong limit theorems for weighted sums of negatively associated random variables..J. Theor. Probab. 21 (2008), 4, 890-909. Zbl 1162.60008, MR 2443640, 10.1007/s10959-007-0128-4 |
Reference:
|
[11] Joag-Dev, K., Proschan, F.: Negative association of random variables, with applications..Ann. Statist. 11 (1983), 1, 286-295. Zbl 0508.62041, MR 0684886, 10.1214/aos/1176346079 |
Reference:
|
[12] Ko, M. H., Kim, T. S., Lin, Z. Y.: The Hàjeck-Rènyi inequality for the AANA random variables and its applications..Taiwan. J. Math. 9 (2005), 1, 111-122. MR 2122907, 10.11650/twjm/1500407749 |
Reference:
|
[13] Shen, A. T., Wu, R. C.: Strong convergence results for weighted sums of $\tilde{\rho }$-mixing random variables..J. Inequal. Appl. 2013 (2013), 1, 327. Zbl 1287.60040, MR 3081708, 10.1186/1029-242x-2013-327 |
Reference:
|
[14] Shen, A. T., Wu, R. C.: Strong and weak convergence for asymptotically almost negatively associated random variables..Discrete Dyn. Nat. Soc. 2013 (2013), 1-7. Zbl 1269.60036, MR 3037709, 10.1155/2013/235012 |
Reference:
|
[15] Shen, A. T., Wu, R. C.: Strong convergence for sequences of asymptotically almost negatively associated random variables..Stochastics 86 (2014), 2, 291-303. Zbl 1312.60024, MR 3180038, 10.1080/17442508.2013.775289 |
Reference:
|
[16] Sung, S. H.: On the strong convergence for weighted sums of random variables..Stat. Pap. 52 (2011), 447-454. Zbl 1247.60041, MR 2795891, 10.1007/s00362-009-0241-9 |
Reference:
|
[17] Sung, S. H.: On the strong convergence for weighted sums of ${{\rho }^{*}}$-mixing random variables..Stat. Pap. 54 (2013), 773-781. MR 3072900, 10.1007/s00362-012-0461-2 |
Reference:
|
[18] Tang, X. F.: Some strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables..J. Inequal. Appl. 2013 (2013), 1, 4. Zbl 1283.60052, MR 3017340, 10.1186/1029-242x-2013-4 |
Reference:
|
[19] Wang, X. J., Hu, S. H., Yang, W. Z.: Complete convergence for arrays of rowwise asymptotically almost negatively associated random variables..Discrete Dyn. Nat. Soc. 2011 (2011), 1-11. Zbl 1235.60026, MR 2846463, 10.1155/2011/717126 |
Reference:
|
[20] Wang, X. J., Hu, S. H., Yang, W. Z., Wang, X. H.: On complete convergence of weighted sums for arrays of rowwise asymptotically almost negatively associated random variables..Abstr. Appl. Anal. 2012 (2012), 1-15. Zbl 1253.60044, MR 2947673, 10.1155/2012/315138 |
Reference:
|
[21] Wang, X. J., Li, X. Q., Yang, W. Z., Hu, S. H.: complete convergence for arrays of rowwise weakly dependent random variables..Appl. Math. Lett. 25 (2012), 11, 1916-1920. Zbl 1251.60025, MR 2957779, 10.1016/j.aml.2012.02.069 |
Reference:
|
[22] Wang, X. H., Shen, A. T., Li, X. Q.: A note on complete convergence of weighted sums for array of rowwise AANA random variables..J. Inequal. Appl. 2013 (2013), 1, 359. Zbl 1295.60038, MR 3101914, 10.1186/1029-242x-2013-359 |
Reference:
|
[23] Wang, Y. B., Yan, J. G., Cheng, F. Y., Su, C.: The strong law of large numbers and the law of the iterated logarithm for product sums of NA and AANA random variables..Southeast Asian Bull. Math. 27 (2003), 2, 369-384. Zbl 1061.60031, MR 2046474 |
Reference:
|
[24] Yang, W. Z., Wang, X. J., Ling, N. X., Hu, S. H.: On complete convergence of moving average process for AANA sequence..Discrete Dyn. Nat. Soc. 2012 (2012), 1-24. Zbl 1247.60043, MR 2923400, 10.1155/2012/863931 |
Reference:
|
[25] Yuan, D. M., An, J.: Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications..Sci. China. Ser. A 52 (2009), 9, 1887-1904. Zbl 1184.62099, MR 2544995, 10.1007/s11425-009-0154-z |
Reference:
|
[26] Yuan, D. M., An, J.: Laws of large numbers for Cesàro alpha-integrable random variables under dependence condition AANA or AQSI..Acta Math. Sinica., English Ser. 28 (2012), 6, 1103-1118. Zbl 1252.60031, MR 2916326, 10.1007/s10114-012-0033-3 |
Reference:
|
[27] Zhou, X. C., Tan, C. C., Lin, J. G.: On the strong laws for weighted sums of ${{\rho }^{*}}$-mixing random variables..J. Inequal. Appl. 2011 (2011), 1, 157816. Zbl 1216.60026, MR 2775040, 10.1155/2011/157816 |
. |