The rates in complete moment convergence for negatively associated sequences

被引：0
作者：
Zhao Y. [1 ]
Qiu Z. [1 ]
Zhang C. [1 ]
Zhao Y. [1 ]
机构：
[1] Department of mathematics, Hangzhou Dianzi University
来源：
Computational and Applied Mathematics | 2010年 / 29卷 / 01期
关键词：
Complete moment convergence; Negatively associated sequences; The rates;
D O I：
10.1590/S1807-03022010000100003
中图分类号：
学科分类号：
摘要：
Let X1, X2,... be a strictly stationary and negatively associated sequence of random variables with mean zero and positive, finite variance, set Sn = X1 + + Xn, Mn = max1≤k≤n |Sk|. Under appropriate moment conditions, we obtain precise rates in law of the logarithm for the moment convergence of Sn and Mn. © 2010 SBMAC.
引用
收藏
页码：31 / 45
页数：14
相关论文
共 22 条
  • [11] Liu W.D., Lin Z.Y., Precise asymptotics for a new kind of complete moment convergence, Statist. Probab. Lett., 76, pp. 1787-1799, (2006)
  • [12] Matula P., A note on the almost sure convergence of sums of negatively dependent random variables, Statist. Probab. Lett., 15, pp. 209-213, (1992)
  • [13] Newman C.M., Asymptotic independent and limit theorems for positively and negatively dependent random variables, Inequalities in Statistics and Probability, pp. 127-140, (1984)
  • [14] Petrov V.V., Limit theorems of probability theory-sequences of independent random variables, (1995)
  • [15] Roussas C.G., Exponential probability inequalities with some applications, Statistics, Probability and Game Theory, pp. 303-319, (1996)
  • [16] Shao Q.M., Su C., The law of the the iterated logarithm for negatively associated random variables, Stochastic Process. Appl., 83, pp. 139-148, (1999)
  • [17] Shao Q.M., A comparison theorem on maximum inequalities between negatively associated sequences and independent random variables, J. Theor. Probab., 13, pp. 343-356, (2000)
  • [18] Su C., Zhao L.C., Wang Y.B., The moment inequalities and weak convergence for negatively associated sequences, Science in China Series A, 39, pp. 1091-1099, (1996)
  • [19] Zhang L.X., The weak convergence for functions of negatively associated random variables, J. Multiv. Anal., 78, pp. 272-298, (2001)
  • [20] Zhang L.X., Wen J.W., A weak convergence for negatively associated fields, Statist. Probab. Lett., 53, pp. 259-267, (2001)
123