Abstract
Consider a sequence of negatively associated and identically distributed random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (0, 2). A Chover’s law of the iterated logarithm is established for negatively associated random variables. Our results generalize and improve those on Chover’s law of the iterated logarithm (LIL) type behavior previously obtained by Mikosch (1984), Vasudeva (1984), and Qi and Cheng (1996) from the i.i.d. case to NA sequences.
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References
K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist., 1983, 11(1): 286–295.
C. M. Newman, Asymptotic Independence and Limit Theorems for Positively and Negatively Dependent Random Variables, in Inequalities in Statistics and Probability, CA, 1984, 127–140.
P. A. Matula, A note on the almost sure convergence of sums of negatively dependent random variables, Statist. Probab. Lett., 1992, 15(3): 209–213.
Q. M. Shao, A comparison theorem on moment inequalities between negatively associated and independent random variables, J. Theoret. Probab., 2000, 13(2): 343–356.
Q. Y. Wu, Complete convergence for NA sequences, China Basic Science, 1999, 2(4): 89–91.
Q. Y. Wu, Strong consistency of M estimator in linear model for negatively associated samples, Journal of Systems Science & Complexity, 2006, 19(4): 592–600.
E. Seneta, Regularly Varying Functions, Lecture Notes in Mathematics 508, Springer, Berlin, 1976.
J. Chover, A law of the iterated logarithm for stable summands, Proc. Amer. Soc., 1966, 17(2): 441–443.
T. Mikosch, On the law of the iterated logarithm for independent random variables outside the domain of partial attraction of the normal law (in Russian), Vestnik Leningrad Univ., 1984, 13: 35–39.
Y. C. Qi and P. Cheng, On the law of the iterated logarithm for the partied sum in the domain of attraction of stable distribution, Chinese Ann. Math., 1996, 17(A): 195–206.
R. Vasudeva, Chover’s law of the iterated logarithm and weak convergence, Acta Math. Hung., 1984, 44(3–4): 215–221.
P. Y. Chen, Chover’s LIL for φ-mixing sequence of heavy-tailed random vectors, Acta Math. Sinica, 2005, 48(3): 447–456.
G. H. Cai, Law of the iterated logarithm for ρ-mixing sequence, Acta Math. Sinica, 2006, 49(1): 155–160.
W. F. Stout, Almost Sure Convergence, New York, Academic Press, 1974.
P. Y. Chen and Y. C. Qi, Chover’s law of the iterated logarithm for weighted sums with application, Sankyhā: The Indian Journal of Statistics, 2006, 68(1): 45–60.
L. De Haan, On Regular Variation and Its Application to the Weak Convergence of Sample Extremes, Mathematical Center Tracts 32, Mathematics Centrum, Amsterdam, 1970.
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This research is supported by the National Natural Science Foundation of China under Grant No. 10661006, the Support Program of the New Century Guangxi China Ten-Hundred-Thousand Talents Project under Grant No. 2005214, and the Guangxi, China Science Foundation under Grant No. 2010GXNSFA013120.
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Wu, Q., Jiang, Y. Chover’s law of the iterated logarithm for negatively associated sequences. J Syst Sci Complex 23, 293–302 (2010). https://doi.org/10.1007/s11424-010-7258-y
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DOI: https://doi.org/10.1007/s11424-010-7258-y