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  Far East Journal of Applied Mathematics  
 ISSN: 0972-0960
 
 
 

     Far East Journal of Applied Mathematics
    Volume 33, Issue 1, Pages 73 - 87 (October 2008)


PRECISE ASYMPTOTICS OF WEIGHTED SUMS OF NEGATIVELY ASSOCIATED RANDOM VARIABLES

Jong-Il Baek (Korea), Hye Yeong Seo (Korea), Gil Hwan Lee (Korea) and Ho Il Chung (Korea)

Received May 21, 2008

References:



[1] K. Alam and K. M. L. Saxena, Positive dependence in multivariate distributions, Comm. Statist. Theor. Math. 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(3) (2003), 901-912.

[3] L. E. Baum and M. Katz, Convergence rates in the law of large numbers, Trans. Amer. Math. Soc. 120 (1965), 108-123.

[4] F. Y. Cheng and Y. B. Wang, Precise asymptotics of partial sums for IID and NA sequences, Acta. Math. Sinica 47 (2004), 965-972.

[5] P. Erdös, On a theorem of Hsu and Robbins, Ann. Math. Statist. 20 (1949), 286-291.

[6] P. Erdös, Remark on my paper, On a theorem of Hsu and Robbins, Ann. Math. Statist. 21 (1950), pp. 138.

[7] A. Gut and A. Spătaru, Precise asymptotics in the law of the iterated logarithm, Ann. Probab. 28 (2000), 1870-1883.

[8] A. Gut and A. Spătaru, Precise asymptotics in the Baum, Katz and Davis law of large numbers, J. Math. Anal. Appl. 248 (2000), 233-246.

[9] A. Gut and J. Steinebach, Convergence rates and precise asymptotics for renewal counting processes and some first passage times, Fields Inst. Comm. 44 (2004), 205-227.

[10] C. C. Heyde, A supplement to the strong law of large numbers, J. Appl. Probab. 12 (1975), 173-175.

[11] P. L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U. S. A. 33 (1947), 25-31.

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

[13] H. Lanzinger and U. Stadtmüller, Refined Baum-Katz laws for weighted sums of iid random variables, Statist. Probab. Lett. 69 (2004), 357-368.

[14] D. L. Li, B. E. Nguyen and A. Rosalsky, A supplement to precise asymptotics in the law of the iterated logarithm, J. Math. Anal. Appl. 302 (2005), 84-96.

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

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

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

[18] Q. M. Shao and C. Su, The law of the iterated logarithm for negatively associated random variables, Stochastic Processes Appli. 83 (1999), 139-148.

[19] F. Spitzer, A combinatorial lemma and its applications to probability theory, Trans. Amer. Math. Soc. 82 (1956), 323-339.

[20] C. Su, L. C. Zhao and Y. B. Wang, Moment inequalities and weak convergence for NA sequences, Sci. China (Ser. A)26 (1996), 1091-1099 (in Chinese).

[21] C. Su and Y. S. Qin, Limit theorems for negatively associated sequences, Chinese Sci. Bull. 42 (1997), 243-246.

Keywords and phrases: precise asymptotics, weighted sum, negatively associated random variables.

 


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