END随机变量移动平均过程的完全矩收敛性

doi:10.6040/j.issn.1671-9352.0.2014.359

Abstract

CLC Number:

O211.4

QIAN Shuo-ge, YANG Wen-zhi. Complete moment convergence of moving average process for END random variables[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 13-18.

[1] LIU Li. Precise large deviations for dependent random variables with heavy tails[J]. Statistics and Probability Letters, 2009, 79(9):1290-1298.
[2] LEHMANN E L. Some concepts of dependence[J]. Annals of Mathematical Statistics, 1966, 37(5):1137-1153.
[3] JOAG-DEV K, PROSCHAN F. Negative association of random variables with applications[J]. Annals of Statistics, 1983, 11(1):286-295.
[4] LIU Li. Necessary and Su-cient conditions for moderate deviations of dependent random variables with heavy tails[J]. Science in China Series A: Mathematics, 2010, 53(6):1421-434.
[5] WANG Xuejun, HU T C, VOLODIN A I, et al. Complete convergence for weighted sums and arrays of row wise extended negatively dependent random variables[J]. Communications in Statistics-Theory and Methods, 2013, 42(13):2391-2401.
[6] WANG Xuejun, WANG Shijie, HU Shuhe, et al. On complete convergence for weighted sums of rowwise extended negatively dependent random variables[J]. Stochastics: An International Journal of Probability and Stochastic Processes, 2013, 85(6):1060-1072.
[7] SHEN Aiting. Probability inequalities for END sequence and their applications[J].Journal of Inequalities and Applications, 2011, 2011:98.1-98.12.
[8] CHEN Yiqing, CHEN Anyue, NG K W. The strong law of large number for extended negatively dependent random variables[J]. The Journal of Applied Probability, 2010, 47:908-922.
[9] WANG Xuejun, ZHENG Lulu, XU Chen, et al. Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors[J]. Statistics A Journal of Theoretical & Applied Statistics, 2015, 49(2):396-407.
[10] HU T C, ROSALSKY A, WANG K L. Complete convergence theorems for extended negatively dependent random variables[J]. Sankhya, 2015, 77A(1):1-29.
[11] 邓新, 夏凤熙, 王学军. END随机变量序列加权和的几乎处处收敛性[J]. 合肥工业大学学报:自然科学版, 2014, 37(6):761-763. DENG Xin, XIA Fengxi, WANG Xuejun. Almost sure convergence of weighted sums of END random variable sequences[J]. Journal of Hefei University of Technology: Natural Science, 2014, 37(6):761-763.
[12] 徐陈, 王学军, 王嫱. END随机变量阵列加权和的完全收敛性[J]. 高校应用数学学报, 2014, 29(3):253-260. XU Chen, WANG Xuejun, WANG Qiang. Complete convergence for weighted sums of arrays of rowwise extended negatively dependent random variables[J]. Applied Mathematics A Journal of Chinese Universities, 2014, 29(3):253-260.
[13] 徐陈, 郑璐璐, 陈志勇, 等. END随机变量序列加权和的完全收敛性[J]. 中国科学技术大学学报, 2014, 44(6):462-467. XU Chen, ZHENG Lulu, CHEN Zhiyong, et al. Complete convergence for weighted sums of arrays of rowwise extended negatively dependent random variables[J]. Journal of University of Science and Technology of China, 2014, 44(6):462-467.
[14] MATULA P. A note on the almost sure convergence of sums of negatively dependent random variables[J]. Statistics and Probability Letters, 1992, 15(3):209-213.
[15] ASADIAN N, FAKOOR V, BOZORGNIA A. Rosenthal's type inequalities for negatively orthant dependent random variables[J]. Journal of the Iranian Statistical Society, 2006, 5(1-2):69-75.
[16] SUNG S H. A note on the complete convergence for weighted sums of negatively dependent random variables[J]. Journal of Inequalities and Applications 2012, 2012:158.
[17] YANG Wenzhi, WANG Xuejun, WANG Xinghui, et al. The consistency for estimator of nonparametric regression model based on NOD errors[J]. Journal of Inequalities and Applications 2012, 2012:140.1-140.13
[18] WU Qunying. Complete convergence for negatively dependent sequences of random variables[J/OL]. Journal of Inequalities and Applications, 2010, 2010:507293.1-507293.10.
[19] WU Qunying. The strong consistency of M estimator in a linear model for negatively dependent random samples[J]. Communications in Statistics-Theory and Methods 2011, 40(3):467-491.
[20] WU Qunying. Probability limit theory of mixing sequences[M]. Beijing: Science Press, 2006.
[21] LI Deli, RAO M B, WANG Xiangchen. Complete convergence of moving average processes[J]. Statistics & Probability Letters, 1992, 14(2):111-114.
[22] LI Yuanxia, ZHANG Lixin. Complete moment convergence of moving-average processes under dependent assumptions[J]. Statistics & Probability Letters, 2004, 70(3):191-197.
[23] ZHANG Lixin. Complete convergence of moving average processes under dependent assumption[J]. Statistics & Probability Letters, 1996, 30(2):165-170
[24] CHEN Pingyan, HU T C, VOLODIN A. Limiting behaviour of moving average processes under φ-mixing assumption[J]. Statistics & Probability Letters, 2009, 79(1):105-111.
[25] ZHOU Xingcai. Complete moment convergence of moving average processes under φ-mixing assumptions[J]. Statistics & Probability Letters, 2010, 80(5-6):285-292.
[26] YANG Wenzhi, HU Shuhe, WANG Xuejun, et al. On complete convergence of moving average process for AANA sequence[J]. Discrete Dynamics in Nature and Society, 2012, Article ID 863931, 24 pages.
[27] SUNG S H. Convergence of moving average processes for dependent random variables[J]. Communications in Statistics-Theory and Methods, 2011, 40:2366-2376.
[28] ADLER A, ROSALSKY A. Some general strong laws for weighted sums of stochastically dominated random variables[J]. Stochastic Analysis and Applications, 1987, 5(1):1-16.
[29] ADLER A, ROSALSKY A, TAYLOR R L. Strong laws of large numbers for weighted sums of random elements in normed linear spaces[J]. International Journal of Mathematics and Mathematical Sciences, 1989, 12(3):507-530.
[30] SUNG S H. Moment inequalities and complete moment convergence[J]. Journal of Inequalities and Applications, 2009, 2009:271265.1-271265.14.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 0

No Suggested Reading articles found!

Complete moment convergence of moving average process for END random variables

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 8

Metrics

Comments

Recommended 0

[1]	DENG Xiao-qin, WU Qun-ying. Precise asymptotics in the complete moment convergence for NA random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(1): 102-110.
[2]	ZHANG Yu, XIAO Ben-qiong, XU Ke, SHEN Ai-ting. Complete moment convergence for arrays of rowwise NSD random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 30-36.
[3]	ZHANG Li-jun, GUO Ming-le. On complete moment convergence of weighted sums for arrays of rowwise asymptotically almost negatively associated random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 42-49.
[4]	TAN Chuang, GUO Ming-le, ZHU Dong-jin. Complete moment convergence of weighted sums of arrays of rowwise ND random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 27-32.
[5]	ZHENG Lu-lu, GE Mei-mei, LIU Yan-fang, WANG Xue-jun. Complete moment convergence for sequences of φ mixing random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 14-19.
[6]	XU Ri-li, GUO Ming-le*. Complete moment convergence of weighted sums of arrays of rowwise ND random variables [J]. J4, 2013, 48(6): 9-13.
[7]	TANG Ling. The consistency of nonparametric regression model for average process of φ-mixing sequence [J]. J4, 2013, 48(3): 89-92.
[8]	TAN Cheng-liang,WU Qun-ying,TIAN Guo-hua . Complete convergence of weighted sums for arrays of row-wise ρ^--mixing random variables [J]. J4, 2008, 43(6): 87-91 .