Complete Moment Convergence of Moving Average Processes Generated by Negatively Associated Sequences

Title & Authors
Complete Moment Convergence of Moving Average Processes Generated by Negatively Associated Sequences
Ko, Mi-Hwa;

Abstract
Let {$\small{X_i,-{\infty}}$ < 1 < $\small{\infty}$} be a doubly infinite sequence of identically distributed and negatively associated random variables with mean zero and finite variance and {$\small{a_i,\;-{\infty}}$ < i < $\small{{\infty}}$} be an absolutely summable sequence of real numbers. Define a moving average process as $Y_n Keywords Moving average process;negatively associated;complete moment convergence;doubly infinite sequence; Language English Cited by References 1. Baek, J. I., Kim, T. S. and Liang, H. Y. (2003). On the convergence of moving average processes under dependent conditions, Australian & New Zealand Journal of Statistics, 45, 331-342. 2. Burton, R. M. and Dehling, H. (1990). Large deviation for some weakly dependent random processes, Statistics & Probability Letters, 9, 397-401. 3. Chen, P. Y., Hu, T. H. and Volodin, A. (2009). Limiting behavior of moving average processes under${\varphi}$-mixing assumption, Statistics & Probability Letters, 79, 105-111. 4. Joag-Dev, K. and Proschan, F. (1983). Negative association of random variables with applications, The Annals of Statistics, 11, 286-295. 5. Kim, T. S. and Baek, J. I. (2001). A central limit theorem for stationary linear processes generated by linearly positively quadrant dependent process, Statistics & Probability Letters, 30, 165-170. 6. Kim, T. S. and Ko, M. H. (2008). Complete moment convergence of moving average processes under dependence assumptions, Statistics & Probability Letters, 78, 839-846. 7. Li, D. L., Rao, M. B. and Wang, X. C. (1992). Complete convergence of moving average processes, Statistics & Probability Letters, 14, 111-114. 8. Li, Y. and Zhang, L. (2004). Complete moment convergence of moving average processes under dependence assumptions, Statistics & Probability Letters, 70, 191-197. 9. Shao, Q. M. (2000). A comparison theorem on maximum inequalities between negatively associated and independent random variables, Journal of Theoretical Probability, 13, 343-356. 10. Zhang, L. (1996). Complete convergence of moving average processes under dependence assumptions, Statistics & Probability Letters, 30, 165-170. 11. Zhou, X. (2010). Complete moment convergence of moving average processes under${\varphi}\$-mixing assumptions, Statistics & Probability Letters, 80, 285-292.