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Chover’s law of the iterated logarithm for negatively associated sequences. (English) Zbl 1205.60069
Summary: 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 {\it T. Mikosch} [Vestn. Leningr. Univ. 1984, No. 19, Mat. Mekh. Astron. No. 4, 82--85 (1984; Zbl 0557.60025)], {\it R. Vasudeva} [Acta Math. Hung. 44, 215--221 (1984; Zbl 0555.60022)], and {\it Y. Qi} and {\it P. Cheng} [Chin. Ann. Math., Ser. A 17, No. 2, 195--206 (1996; Zbl 0861.60043)] from the i.i.d. case to NA sequences.

60F15Strong limit theorems
Full Text: DOI
[1] K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist., 1983, 11(1): 286--295. · Zbl 0508.62041 · doi:10.1214/aos/1176346079
[2] 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.
[3] 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. · Zbl 0925.60024 · doi:10.1016/0167-7152(92)90191-7
[4] Q. M. Shao, A comparison theorem on moment inequalities between negatively associated and independent random variables, J. Theoret. Probab., 2000, 13(2): 343--356. · Zbl 0971.60015 · doi:10.1023/A:1007849609234
[5] Q. Y. Wu, Complete convergence for NA sequences, China Basic Science, 1999, 2(4): 89--91.
[6] 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. · Zbl 1123.62022 · doi:10.1007/s11424-006-0592-4
[7] E. Seneta, Regularly Varying Functions, Lecture Notes in Mathematics 508, Springer, Berlin, 1976. · Zbl 0324.26002
[8] J. Chover, A law of the iterated logarithm for stable summands, Proc. Amer. Soc., 1966, 17(2): 441--443. · Zbl 0144.40503 · doi:10.1090/S0002-9939-1966-0189096-2
[9] 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.
[10] 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.
[11] R. Vasudeva, Chover’s law of the iterated logarithm and weak convergence, Acta Math. Hung., 1984, 44(3--4): 215--221. · Zbl 0555.60022 · doi:10.1007/BF01950273
[12] P. Y. Chen, Chover’s LIL for {$\phi$}-mixing sequence of heavy-tailed random vectors, Acta Math. Sinica, 2005, 48(3): 447--456. · Zbl 1124.60300
[13] G. H. Cai, Law of the iterated logarithm for {$\rho$}-mixing sequence, Acta Math. Sinica, 2006, 49(1): 155--160. · Zbl 1121.60306
[14] W. F. Stout, Almost Sure Convergence, New York, Academic Press, 1974. · Zbl 0321.60022
[15] 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. · Zbl 1192.60058
[16] L. De Haan, On Regular Variation and Its Application to the Weak Convergence of Sample Extremes, Mathematical Center Tracts 32, Mathematics Centrum, Amsterdam, 1970. · Zbl 0226.60039