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http://dx.doi.org/10.5351/CKSS.2005.12.1.117

On the Functional Central Limit Theorem of Negatively Associated Processes  

Baek Jong Il (Division of Mathematics & Informational Statistics, and Institute of Basic Natural Science, Wonkwang University)
Park Sung Tae (Division of Business Adminstration, Wonkwang University)
Lee Gil Hwan (Division of Mathematics & Informational Statistics, Wonkwang University)
Publication Information
Communications for Statistical Applications and Methods / v.12, no.1, 2005 , pp. 117-123 More about this Journal
Abstract
A functional central limit theorem is obtained for a stationary linear process of the form $X_{t}= \sum\limits_{j=0}^\infty{a_{j}x_{t-j}}$, where {x_t} is a strictly stationary sequence of negatively associated random variables with suitable conditions and {a_j} is a sequence of real numbers with $\sum\limits_{j=0}^\infty|a_{j}|<\infty$.
Keywords
Functional central limit theorem; Linear process; Negatively associated random variables;
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  • Reference
1 Billingsley, P.(1968). Convergence of probability measure. Wiley, New York
2 Newman, C. M.(1984). Asymptotic independence and limit theorems for positively and negatively dependent random variables. Inequalities in statistics and probability, ed Y. L. Tong. IMS Lecture Notes-Monograph Series, 5, 127-140. Hayward, CA
3 Su, C., Zhao, L., Wang, Y.(1997). Moment inequalities and weak convergence for negatively associated sequences. Science in China Series A., 26, 1091-1099
4 Yuan, M., Su, C., Hu, T.(2003). A central limit theorem for random fields of negatively associated processes. Journal of Theoretical Probability, 16, no. 2, 309-323   DOI   ScienceOn
5 Baek, J. I., Kim, T. S., Liang, H. Y.(2003). On the convergence of moving average processes under dependent conditions. Australian & New Zealand. Journal of Statistics, 45, no. 3, 331-342   DOI   ScienceOn
6 Fakhre-Zakeri, I., Farshidi, J.(1993) A central limit theorem with random indices for stationary linear processes. Statistics & Probability Letters, 17, no. 2, 91-95   DOI   ScienceOn
7 Fakhre-Zakeri, I., Lee, S.(1997). A random functional central limit theorem for stationary linear processes generated by martingales. Statistics Probability Letters, 35, no. 4, 417-422   DOI   ScienceOn
8 Hannan, E. J.(1970). Multivariate time series. Wiley, New York
9 Lehmann, E. L.(1966). Some concepts of dependence. Ann Math Statist. 37, 1137-1153   DOI   ScienceOn
10 Liang, H. Y., Su, C.(1999). Complete convergence for weighted sums of NA sequences. Statistics Probability Letters, 45, no. 1, 85-95   DOI   ScienceOn