TY  - JOUR
T1  - Complete qth moment convergence of weighted sums for arrays of row-wise extended negatively dependent random variables
AU  - Guo, M. L..
PY  - 2014
DA  - April
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 323
EP  - 335
VL  - 43
IS  - 2
LA  - en
AB  - In this paper, the complete qth moment convergence of weighted sumsfor arrays of row-wise extended negatively dependent (abbreviated toEND in the following) random variables is investigated. By usingHoffmann-Jφrgensen type inequality and truncation method, some general results concerning complete qth moment convergence of weightedsums for arrays of row-wise END random variables are obtained. Astheir applications, we extend the corresponding result of Wu (2012) tothe case of arrays of row-wise END random variables. The complete qthmoment convergence of moving average processes based on a sequenceof END random variables is obtained, which improves the result of Liand Zhang (2004). Moreover, the Baum-Katz type result for arrays ofrow-wise END random variables is also obtained.
KW  - END random variables
KW  - Weighted sums
KW  - Complete moment convergence
KW  - Complete convergence
CR  - 1] Hsu, P. L. and Robbins, H. Complete convergence and the law of large numbers. Proc. Natl.
Acad. Sci. U.S.A., 33(2), 25–31, 1947.
CR  - [2] Baum, L. E. and Katz, M. Convergence rates in the law of large numbers. Trans. Am.
Math. Soc., 120(1), 108–123, 1965.
CR  - [3] Liu, L. Precise large deviations for dependent random variables with heavy tails. Statist.
Probab. Lett., 79(9), 1290–1298, 2009.
CR  - [4] Lehmann, E. L. Some concepts of dependence. Ann. Math. Statist., 37(5), 1137–1153,
1966.
CR  - [5] Joag-Dev, K. and Proschan, F. Negative association of random variables with applications.
Ann. Statist., 11(1), 286–295, 1983.
334
CR  - [6] Shen, A. T. Probability inequalities for END sequence and their applications. J. Inequal.
Appl., 2011, 98, 2011.
CR  - [7] Chen, Y. Q. and Chen, A. Y. and Ng, K. W. The strong law of large numbers for extend
negatively dependent random variables. J. Appl. Prob., 47(4), 908–922, 2010.
CR  - [8] Baek, J. I., Choi, I. B. and Niu, S. l. On the complete convergence of weighted sums for
arrays of negatively associated variables. J. Korean Stat. Soc., 37(1), 73–80, 2008.
CR  - [9] Baek, J. I. and Park, S. T. Convergence of weighted sums for arrays of negatively dependent
random variables and its applications. J. Stat. Plan. Infer., 140(9), 2461–2469, 2010.
CR  - [10] Wu, Q. A complete convergence theorem for weighted sums of arrays of rowwise negatively
dependent random variables. J. Inequal. Appl.,2012: 50, 2012.
CR  - [11] Chow, Y. S. On the rate of moment convergence of sample sums and extremes. Bull. Inst.
Math. Acad. Sinica, 16(3), 177–201, 1988.
CR  - [12] Liang, H. Y., Li, D. L. and Rosalsky, A. Complete moment convergence for sums of negatively associated random variables. Acta Math. Sinica, English Series, 26(3), 419–432,
2010.
CR  - [13] Sung, S. H. Complete qth moment convergence for arrays of random variables. J. Inequal.
Appl., 2013, 24, 2013.
CR  - [14] Guo, M. L. On complete moment convergence of weighted sums for arrays of row-wise
negatively associated random variables. Stochastics: Int. J. Probab. Stoch. Proc., 86(3),
415-428, 2014.
CR  - [15] Li, Y. X. and Zhang, L. X. Complete moment convergence of moving-average processes
under dependence assumptions. Statist. Probab. Lett., 70(3), 191–197, 2004.
CR  - [16] Wu, Q. Y. Probability Limit Theory for Mixed Sequence. China Science Press, Beijing, 2006.
UR  - https://dergipark.org.tr/en/pub/hujms/issue//524485
L1  - https://dergipark.org.tr/en/download/article-file/644889
ER  -