Browse > Article
http://dx.doi.org/10.5351/CKSS.2012.19.5.647

On Convergence of Weighted Sums of LNQD Random  

Kim, So-Youn (School of mathematical Science and Institute of Basic Natural Science, Wonkwang University)
Baek, Jong-Il (School of mathematical Science and Institute of Basic Natural Science, Wonkwang University)
Publication Information
Communications for Statistical Applications and Methods / v.19, no.5, 2012 , pp. 647-654 More about this Journal
Abstract
We discuss the strong convergence for weighted sums of linearly negative quadrant dependent(LNQD) random variables under suitable conditions and the central limit theorem for weighted sums of an LNQD case is also considered. In addition, we derive some corollaries in LNQD setting.
Keywords
Complete convergence; almost sure convergence; arrays; negative associated random variables; linearly negative quadrant random variables;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Liaug, H. Y, Zhang, D. X. and Baek, J. I. (2004). Convergence of weighted sums for dependent random variables, Journal of the Korean Mathematical Society, 41,883-894.   과학기술학회마을   DOI   ScienceOn
2 Magda, P. and Sergey, U. (1997). Central limit theorem for linear processes, The Annals of Probability, 25, 443-456.   DOI   ScienceOn
3 Newman, C. M. (1984). Asymptotic independence and limit theorems for positively and negatively dependent random variables. In Y L. Tong(Ed.)., Statistics and Probability, 5 127-140.
4 Pruitt, W. E. (1966). Summability of independence of random variables, Journal of Mathematics and Mechanics, 15, 769-776.
5 Rohatgi, V. K. (1971). Convergence of weighted sums of independent random variables, Mathematical Proceedings of the Cambridge Philosophical Society, 69, 305-307.   DOI
6 Waug, J. and Zhaug, L. (2006). A Berry-Esseen theorem for weakly negatively dependent random variables and its applications, Acta Mathematica Hungarica, 110, 293-308.   DOI
7 Waug, X., Rao, M. B. and Yang, X. (1993). Convergence rates on strong laws of large numbers for arrays of rowwise independent elements, Stochastic Analysis and Applications, 11, 115-132.   DOI   ScienceOn
8 Cai, Z. and Roussas, G. G. (1997). Smooth estimate of quantiles under association, Statistics & Probability Letters, 36, 275-287.   DOI   ScienceOn
9 Ghosal, S. and Chandra, T. K. (1998). Complete convergence of martingale arrays, Journal of Theoretical Probability, 11, 621-631.   DOI
10 Gut, A. (1992). Complete convergence for arrays, Periodica Mathematica Hungarica, 25, 51-75.   DOI
11 Hsu, P. L. and Robbins, H. (1947). Complete convergence and the law of large numbers, In Proceedings of the National Academy of Sciences of the United States of America, 33, 25-31.   DOI   ScienceOn
12 Ko, M. H., Ryu, D.-H. and Kim, T.-S. (2007). Limiting behaviors of weighted sums for linearly negative quadrant dependent dependent random variables, Taiwanese Journal of Mathematics, 11, 511-522.
13 Hu, T. C., Li, D., Rosalsky, A. and Volodin, A. (2001). On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements, Theory of Probability and Its Applications, 47, 455-468.
14 Hu, T. C., Rosalsky, A., Szynal, D. aud Volodin, A. (1999). On complete convergence for arrays of rowwise independent random elements in Banach spaces, Stochastic Analysis and Applications, 17, 963-992.   DOI   ScienceOn
15 Joag Dev, K. and Proschau, F. (1983). Negative association of random variables with applications, The Annals of Statistics, 11, 286-295.   DOI   ScienceOn
16 Kuczmaszewska, A. and Szynal, D. (1994). On complete convergence in a Banach space, International Journal of Mathematics and Mathematical Sciences, 17, 1-14.   DOI   ScienceOn
17 Lehmann, E. L. (1966). Some concepts of dependence, The Annals of Mathematical Statistics, 37, 1137-1153.   DOI
18 Baek, J. I., Park, S. T., Chung, S. M., Liang, H. Y. and Lee, C. Y. (2005). On the complete convergence of weighted sums for dependent random variables, Journal of the Korean Statistical Society, 34, 21-33.   과학기술학회마을
19 Ahmed, S. E., Antonini, R. G. and Volodin, A. (2002). On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes, Statistics & Probability Letters, 58, 185C194.   DOI   ScienceOn
20 Antonini, R. G., Kwon, J. S., Sung, S. H. and Volodin, A. I. (2001). On the strong convergence of weighted sums, Stochastic Analysis and Applications, 19, 903-909.   DOI   ScienceOn
21 Billingsley, P. (1968). Convergence of Probability Measures, John Wiley & Sons, New York.