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)].


60E15 Inequalities; stochastic orderings
62E20 Asymptotic distribution theory in statistics
62G20 Asymptotic properties of nonparametric inference
Full Text: DOI


[1] Bozorgnia, A.; Patterson, R. F.; Taylor, R. L., Limit theorems for dependent random variables, (World Congress Nonlinear Analysts’ 92 (1996)), 1639-1650 · Zbl 0845.60010
[2] Christofides, T. C.; Hadjikyriakou, M., Exponential inequalities for N-demimartingales and negatively associated random variables, Statist. Probab. Lett., 79, 2060-2065 (2009) · Zbl 1180.60016
[3] Fujioka, T., Asymptotic approximations of the inverse moment of the non-central chi-squared variable, J. Japan Statist. Soc., 31, 99-109 (2001) · Zbl 1031.62011
[4] Garcia, N. L.; Palacios, J. L., On inverse moments of nonnegative random variables, Statist. Probab. Lett., 53, 235-239 (2001) · Zbl 0991.60003
[5] Gupta, R. C.; Akman, O., Statistical inference based on the length-biased data for the inverse Gaussian distribution, Statistics, 31, 325-337 (1998) · Zbl 0930.62020
[6] Hoeffding, W., Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc., 58, 13-30 (1963) · Zbl 0127.10602
[7] Hu, S. H.; Chen, G. J.; Wang, X. J.; Chen, E. B., On inverse moments of nonnegative weakly convergent random variables, Acta Math. Appl. Sin., 30, 361-367 (2007), (in Chinese) · Zbl 1141.60309
[8] Jurlewicz, A.; Weron, K., Relaxation of dynamically correlated clusters, J. Non-Cryst. Solids, 305, 112-121 (2002)
[9] Joag-Dev, K.; Proschan, F., Negative association of random variables with applications, Ann. Statist., 11, 1, 286-295 (1983) · Zbl 0508.62041
[10] Kaluszka, M.; Okolewski, A., On Fatou-type lemma for monotone moments of weakly convergent random variables, Statist. Probab. Lett., 66, 45-50 (2004) · Zbl 1116.60308
[11] Marciniak, E.; Wesolowski, J., Asymptotic Eulerian expansions for binomial and negative binomial reciprocals, Proc. Amer. Math. Soc., 127, 3329-3338 (1999) · Zbl 0930.60004
[12] Mendenhall, W.; Lehman, E. H., An approximation to the negative moments of the positive binomial useful in life-testing, Technometrics, 2, 227-242 (1960) · Zbl 0105.12305
[13] Pittenger, A. O., Sharp mean-variance bounds for Jensen-type inequalities, Statist. Probab. Lett., 10, 91-94 (1990) · Zbl 0705.60017
[14] Ramsay, C. M., A note on random survivorship group benefits, ASTIN Bull., 23, 149-156 (1993)
[15] Wooff, D. A., Bounds on reciprocal moments with applications and developments in Stein estimation and post-stratification, J. R. Stat. Soc. Ser. B, 47, 362-371 (1985) · Zbl 0603.62016
[16] Wu, T. J.; Shi, X. P.; Miao, B. Q., Asymptotic approximation of inverse moments of nonnegative random variables, Statist. Probab. Lett., 79, 1366-1371 (2009) · Zbl 1168.60340
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