Previous |  Up |  Next

Article

Title: On the strong convergence for weighted sums of asymptotically almost negatively associated random variables (English)
Author: Huang, Haiwu
Author: Deng, Guangming
Author: Zhang, QingXia
Author: Jiang, Yuanying
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 50
Issue: 3
Year: 2014
Pages: 393-407
Summary lang: English
.
Category: math
.
Summary: Applying the moment inequality of asymptotically almost negatively associated (AANA, in short) random variables which was obtained by Yuan and An (2009), some strong convergence results for weighted sums of AANA random variables are obtained without assumptions of identical distribution, which generalize and improve the corresponding ones of Zhou et al. (2011), Sung (2011, 2012) to the case of AANA random variables, respectively. (English)
Keyword: AANA random variables
Keyword: strong convergence
Keyword: weighted sums
MSC: 60F15
idZBL: Zbl 1301.60030
idMR: MR3245537
DOI: 10.14736/kyb-2014-3-0393
.
Date available: 2014-07-29T13:13:23Z
Last updated: 2016-01-03
Stable URL: http://hdl.handle.net/10338.dmlcz/143882
.
Reference: [1] Bai, Z. D., Cheng, P. E.: Marcinkiewicz strong laws for linear statistics..Stat. Probab. Lett. 46 (2000), 105-112. Zbl 0960.60026, MR 1748864, 10.1016/S0167-7152(99)00093-0
Reference: [2] 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: [3] Cuzick, J.: A strong law for weighted sums of i.i.d. random variables..J. Theoret. Probab. 8 (1995), 3, 625-641. Zbl 0833.60031, MR 1340830, 10.1007/BF02218047
Reference: [4] 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: [5] Hu, X. P., Fang, G. H., Zhu, D. J.: Strong convergence properties for asymptotically almost negatively associated sequence..Discrete Dyn. Nat. Soc. 2012 (2012), Article ID 562838, 8 pages, doi:10.1155/2012/562838. Zbl 1257.62066, MR 2993321, 10.1155/2012/562838
Reference: [6] 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
Reference: [7] Shen, A. T., Wu, R. C.: Strong and weak convergence for asymptotically almost negatively associated random variables..Discrete Dyn. Nat. Soc. 2013 (2013), Article ID235012, 7 pages, doi:10.1155/2013/235012. Zbl 1269.60036, MR 3037709, 10.1155/2013/235012
Reference: [8] Sung, S. H.: On the strong convergence for weighted sums of random variables..Statist. Pap. 52 (2011), 447-454. Zbl 1247.60041, MR 2795891, 10.1007/s00362-009-0241-9
Reference: [9] Sung, S. H.: On the strong convergence for weighted sums of ${{\rho }^{*}}$-mixing random variables..Statist. Pap. 54 (2013), 773-781. MR 3072900, 10.1007/s00362-012-0461-2
Reference: [10] Tang, X. F.: Some strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables..J. Inequal. Appl. 2013 (2013), doi:10.1186/1029-242X-2013-4. Zbl 1283.60052, MR 3017340, 10.1186/1029-242X-2013-4
Reference: [11] Wang, X. J., Hu, S. H., Shen, Y., Yang, W. Z.: Some new results for weakly dependent random variable sequences..Chinese J. Appl. Probab. Stat. 26 (2010), 6, 637-648. Zbl 1240.60085, MR 2760173
Reference: [12] 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: [13] Wang, X. J., Hu, S. H., Yang, W. Z.: Convergence properties for asymptotically almost negatively associated sequence..Discrete Dyn. Nat. Soc. 2010 (2010), Article ID 218380, 15 pages. Zbl 1207.60025, MR 2770590
Reference: [14] 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), Article ID 717126, 11 pages, doi: 10.1155/2011/717126. Zbl 1235.60026, MR 2846463, 10.1155/2011/717126
Reference: [15] 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), Article ID 315138, 15 pages, doi:10.1155/2012/315138. Zbl 1253.60044, MR 2947673, 10.1155/2012/315138
Reference: [16] Wang, X. J., Li, X. Q., Yang, W. Z., Hu, S. H.: On 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: [17] 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: [18] 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), Article ID 863931, 24 pages, doi:10.1155/2012/863931. Zbl 1247.60043, MR 2923400, 10.1155/2012/863931
Reference: [19] Wu, W. B.: On the strong convergence of a weighted sum..Stat. Probab. Lett. 44 (1999), 19-22. Zbl 0951.60027, MR 1706378
Reference: [20] Wu, Q. Y.: Complete convergence for negatively dependent sequences of random variables..J. Inequal. Appl. 2010 (2010), Article ID 507293, 10 pages, doi: 10.1155/2010/507293. Zbl 1202.60050, MR 2611036, 10.1155/2010/507293
Reference: [21] Wu, Q. Y.: A strong limit theorem for weighted sums of sequences of negatively dependent random variables..J. Inequal. Appl. 2010 (2010), Article ID 383805, 8 pages, doi: 10.1155/2010/383805. Zbl 1202.60044, MR 2678912, 10.1155/2010/383805
Reference: [22] Yuan, D. M., An, J.: Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications..Sci. China (Ser. A): Mathematics 52 (2009), 9, 1887-1904. Zbl 1184.62099, MR 2544995, 10.1007/s11425-009-0154-z
Reference: [23] Yuan, D. M., An, J.: Laws of large numbers for Cesèaro alpha-integrable random variables under dependence condition AANA or AQSI..Acta Math. Sinica., English Series 28 (2012), 6, 1103-1118. MR 2916326, 10.1007/s10114-012-0033-3
Reference: [24] Yuan, D. M., Wu, X. S.: Limiting behavior of the maximum of the partial sum for asymptotically negatively associated random variables under residual Cesèaro alpha-integrability assumption..J. Stat. Plan. Inference 140 (2010), 9, 2395-2402. MR 2644059, 10.1016/j.jspi.2010.02.011
Reference: [25] 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), Article ID 157816, 8 pages, doi: 10.1155/2011/157816. Zbl 1216.60026, MR 2775040, 10.1155/2011/157816
.

Files

Files Size Format View
Kybernetika_50-2014-3_6.pdf 294.7Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo