Convergence of weighted sums for dependent random variables

Journal of the Korean Mathematical Society

Volumn 41, Issue 5, 2004, Pages 883-894

  Liang, Han Ying ^a   Zhang, Dong Xia ^a   Baek, Jong Il ^b  

^a TONGJI UNIVERSITY   (China)

^b Wonkwang University   (South Korea)

Author keywords

Central limit theorem; Ces ro mean; Negatively associated random variable; Strong convergence; Weighted sum

Indexed keywords

EID: 20444429402     PISSN: 03049914     EISSN: None     Source Type: Journal    
DOI: 10.4134/JKMS.2004.41.5.883     Document Type: Article

References (23)

1. K. Alam and K. M. L. Saxena, Positive dependence in multivariate distributions, Comm. Statist. Theory Methods A10 (1981), 1183-1196.
2. P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968.
3. Z. W. Cai and G. G. Roussas, Berry-Esseen bounds for smooth estimator of distribution function under association, Nonparametric Statist. 11 (1999), 79-106.
4. Y. S. Chow and T. L. Lai, Limiting behavior of weighted sums of independent random variables, Ann. Probab. 1 (1973), 810-824.
5. Y. Déniel and Y. Derriennic, Sur la convergence presque sure, au sens de Cesàro d'ordre α, 0 < α < 1, de variables aléatoires et indépendantes et identiquement distribuées, Probab. Theory Related Fields 79 (1988), 629-636.
6. P. Hall and C. C. Heyde, Martingale Limit Theory and Its Applications, New York, Academic Press, 1980.
7. B. Heinkel, An infinite-dimensional law of large numbers in Cesàro's sense, J. Theoret. Probab. 3 (1990), 533-546.
8. K. Joag-Dev and F. Proschan, Negative association of random, variables with applications, Ann. Statist. 11 (1983), 286-295.
9. T.-S. Kim and J.-I. Baek, A central limit theorem for stationary linear processes generated by linearly positively quadrant dependent process, Statist. Probab. Lett. 51 (2001), 299-305.
10. D. L. Li, M. B. Rao, T. F. Jiang and X. C. Wang, Complete convergence and almost sure conver-gence of weighted sums of random, variables, J. Theoret. Probab. 8 (1995), 49-76.
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. H. Y. Liang and B. Y. Jing, Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences, Submitted, 2002.
14. G. G. Lorentz, Borel and Banach properties of methods of summation, Duke Math. J. 22 (1955), 129-141.
15. P. Matula, A note on the almost sure convergence of sums of negatively dependences random variables, Statist. Probab. Lett. 15 (1992), 209-213.
16. D. S. Mitrinovic, Analytic Inequalities, New York, Springer, 1970.
17. M. Peligrad and S. Utev, Central limit theorem for linear processes, Ann. Probab. 25 (1997), no. 1, 443-456.
18. P. C. B. Phillips and V. Solo, Asymptotics for linear processes, Ann. Statist. 20 (1992), 971-1001.
19. G. G. Roussas, Asymptotic normality of random fields of positively or negatively associated processes, J. Multivariate Anal. 50 (1994), 152-173.
20. Q. M. Shao, A comparison theorem on maximum inequalities between negatively associated and independent random, variables, J. Theoret. Probab. 13 (2000), 343-356.
21. Q. M. Shao and C. Su, The law of the iterated logarithm for negatively associated random variables, Stochastic Process. Appl. 83 (1999), 139-148.
22. W. F. Stout, Almost Sure Convergence, Academic Press, New York, 1974.
23. C. Su, L. C. Zhao and Y. B. Wang, Moment inequalities and week convergence for negatively associated sequences, Sci. China Ser. A 40 (1997), 172-182.