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A remark on the exponential inequality for negatively associated random variables. (English) Zbl 1293.60042
Summary: We give an exponential inequality for negatively associated random variables. The inequality improves the corresponding result which was obtained in [T.-S. Kim and H.-C. Kim, Commun. Korean Math. Soc. 22, No. 2, 315–321 (2007; Zbl 1168.60335)]. We also obtain the convergence rate \(n^{-1/2}(\log n)^{3/2}\) for the strong law of large numbers, which improves the corresponding one obtained by the authors in the above-cited reference.

MSC:
60F15 Strong limit theorems
62G20 Asymptotic properties of nonparametric inference
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[1] Kim, T.S.; Kim, H.C., On the exponential inequality for negatively dependent sequence, Korean mathematical society. communications, 22, 2, 315-321, (2007) · Zbl 1168.60335
[2] Matula, P., A note on the almost sure convergence of sums of negatively dependent random variables, Statistics & probability letters, 15, 3, 209-213, (1992) · Zbl 0925.60024
[3] Oliveira, P.D., An exponential inequality for associated variables, Statistics & probability letters, 73, 189-197, (2005) · Zbl 1070.60019
[4] Su, Chun; Zhao, Lincheng; Wang, Yuebao, Moment inequalities for NA sequence and weak convergence, Science in China (series A), 26, 12, 1091-1099, (1996), (in Chinese)
[5] Shao, Qiman; Su, Chun, The law of the iterated logarithm for negatively associated random variables, Stochastic processes and their applications, 83, 139-148, (1999) · Zbl 0997.60023
[6] Shao, Qiman, A comparison theorem on maximal inequalities between negatively associated and independent random variables, Journal of theoretical probability, 13, 2, 343-356, (2000) · Zbl 0971.60015
[7] Yang, Shanchao, Moment inequalities for partial sums of random variables, Science in China (series A), 44, 1-6, (2001) · Zbl 0997.60010
[8] Yang, Shanchao; Wang, Yuebao, Strong consistency of regression function estimator for negatively associated samples, Acta mathematicae applicatae sinica, 22, 4, 522-530, (1999), (in Chinese) · Zbl 0961.62033
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