Xing, Guodong; Yang, Shanchao; Liu, Ailin; Wang, Xiangping A remark on the exponential inequality for negatively associated random variables. (English) Zbl 1293.60042 J. Korean Stat. Soc. 38, No. 1, 53-57 (2009). 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. Cited in 2 ReviewsCited in 12 Documents MSC: 60F15 Strong limit theorems 62G20 Asymptotic properties of nonparametric inference Keywords:negatively associated; strictly stationary; exponential inequality; convergence rate PDF BibTeX XML Cite \textit{G. Xing} et al., J. Korean Stat. Soc. 38, No. 1, 53--57 (2009; Zbl 1293.60042) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.