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Exponential inequalities and inverse moment for NOD sequence. (English) Zbl 1186.60015
Summary: Some exponential inequalities for a negatively orthant dependent sequence are obtained. By using the exponential inequalities, we study the asymptotic approximation of inverse moment for negatively orthant dependent random variables, which generalizes and improves the corresponding results of M: Kaluszka and A. Okolewski [Statist. Probab. Lett. 66, No. 1, 45–50 (2004; Zbl 1116.60308)], S. Hu, G. J. Chen, X. J. Wang and E. B. Chen [Acta Math. Appl. Sin. 30, No. 2, 361–367 (2007; Zbl 1141.60309)] and T. J. Wu, X. P. Shi and B. Q. Miao, Statist. Probab. Lett. 79, No. 11, 1366–1371 (2009, Zbl 1168.60340)].

MSC:
60E15Inequalities in probability theory; stochastic orderings
62E20Asymptotic distribution theory in statistics
62G20Nonparametric asymptotic efficiency
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