ON THE ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF NEGATIVELY ASSOCIATED RANDOM VARIABLES

Title & Authors
ON THE ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF NEGATIVELY ASSOCIATED RANDOM VARIABLES
BAEK, JONG-IL; PARK, SUNG-TAE; CHUNG, SUNG-MO; SEO, HYE-YOUNG;

Abstract
Let $\small{{X,\;X_n|n\;\geq\;1}}$ be a sequence of identically negatively associated random variables under some conditions. We discuss strong laws of weighted sums for arrays of negatively associated random variables.
Keywords
strong laws of large numbers;almost sure convergence;arrays;negatively associated random variables;
Language
English
Cited by
1.
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호남수학학술지, 2012. vol.34. 2, pp.241-252
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ON ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF LNQD RANDOM VARIABLES, Honam Mathematical Journal, 2012, 34, 2, 241
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References
1.
K. Alam and K. M. L. Saxena, Positive dependence in multivariate distributions, Comm. Statist. Theory Methods A10 (1981), 1183-1196

2.
J. I. Baek, T. S. Kim and H. Y. Liang, On the convergence of moving average processes under dependent conditions, Aust. N. Z. J. Stat. 45 (2003), no. 3, 331-342

3.
Z. D. Bai and P. E. Cheng, Marcinkiewicz strong lawss for linear statistics, Statist. Probab. Lett. 46 (2000), 105-112

4.
Z. D. Bai, P. E. Cheng, and C. H. Zhang, An extension of the Hardy-Littlewood strong law, Statist. Sinica, 1997, 923-928

5.
P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968

6.
H. W. Block, T. H. Savits, and M. Shaked, Some concepts of negative dependence, Ann. Probab. 10 (1982), 765-772

7.
P. E. Cheng, A note on strong convergence rates in nonparametric regression, Statist. Probab. Lett. 24 (1995), 357-364

8.
J. Cuzick, A strong law for weighted sums of i.i.d. random variables, J. Theoret. Probab. 8 (1995), 625-641

9.
T. C. Hu, F. Moricz, and R. L. Taylor, Strong laws of large numbers for arrays of rounuise independent random variables, Statistics Technical Report 27. University of Georgia, 1986

10.
K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist. 11 (1983), 286-295

11.
H. Y. Liang and C. Su, Complete convergence for weighted sums of NA sequences, Statist. Probab. Lett. 45 (1999), 85-95

12.
H. Y. Liang, Complete convergence for weighted sums of negatively associated random variables, Statist. Probab. Lett. 48 (2000), 317-325

13.
P. Matula, A note on the almost sure convergence of sums of negatively dependences random variables, Statist. Probab. Lett. 15 (1992), 209-213

14.
C. M. Newman and Y. L. Tong, Asymptotic independence and limit theorems for positively and negatively dependent random variables (IMS, Hayward, CA), 1984, 127-140

15.
G. G. Roussas, Asymptotic normality of random fields of positively or negatively associated processes, J. Multivariate Anal. 50 (1994), 152-173

16.
Q. M. Shao, A comparison theorem on moment inequalities between negatively associated and independent random variables, J. Theoret. Probab. 13 (2000), 343-356

17.
C. Su, L. C. Zhao, and Y. B. Wang, Moment inequalities and weak convergence for negatively associated sequences, Sci. China Ser. A 40 (1997), 172-182

18.
S. Sung, Strong laws for weighted sums of i.i.d.random variables, Statist. Probab. Lett. 52 (2001), 413-419