On inverse moments for a class of nonnegative random variables. (English) Zbl 1205.60041

Sung, Soo Hak

J. Inequal. Appl. 2010, Article ID 823767, 13 p. (2010).

Summary: Using exponential inequalities, T.-J. Wu, X. Shi and B. Miao [Stat. Probab. Lett. 79, No. 11, 1366–1371 (2009; Zbl 1168.60340)] and X. Wang, S. Hu, W. Yang and N. Ling [Stat. Probab. Lett. 80, No. 5–6, 452–461 (2010; Zbl 1186.60015)] obtained asymptotic approximations of inverse moments for nonnegative independent random variables and nonnegative negatively orthant dependent random variables, respectively. In this paper, we improve and extend their results to nonnegative random variables satisfying a Rosenthal-type inequality.

MSC:

60E15	Inequalities; stochastic orderings
62E20	Asymptotic distribution theory in statistics

Citations:

Zbl 1168.60340; Zbl 1186.60015

References:

[1]	Wooff, DA, Bounds on reciprocal moments with applications and developments in Stein estimation and post-stratification, Journal of the Royal Statistical Society. Series B, 47, 362-371, (1985) · Zbl 0603.62016
[2]	Pittenger, AO, Sharp Mean-variance bounds for Jensen-type inequalities, Statistics & Probability Letters, 10, 91-94, (1990) · Zbl 0705.60017
[3]	Marciniak, E; Wesołowski, J, Asymptotic Eulerian expansions for binomial and negative binomial reciprocals, Proceedings of the American Mathematical Society, 127, 3329-3338, (1999) · Zbl 0930.60004
[4]	Fujioka, T, Asymptotic approximations of the inverse moment of the noncentral chi-squared variable, Journal of the Japan Statistical Society, 31, 99-109, (2001) · Zbl 1031.62011
[5]	Jurlewicz, A; Weron, K, Relaxation of dynamically correlated clusters, Journal of Non-Crystalline Solids, 305, 112-121, (2002)
[6]	Ramsay, CM, A note on random survivorship group benefits, ASTIN Bulletin, 23, 149-156, (1993)
[7]	Garcia, NL; Palacios, JL, On inverse moments of nonnegative random variables, Statistics & Probability Letters, 53, 235-239, (2001) · Zbl 0991.60003
[8]	Kaluszka, M; Okolewski, A, On Fatou-type lemma for monotone moments of weakly convergent random variables, Statistics & Probability Letters, 66, 45-50, (2004) · Zbl 1116.60308
[9]	Hu, SH; Chen, GJ; Wang, XJ; Chen, EB, On inverse moments of nonnegative weakly convergent random variables, Acta Mathematicae Applicatae Sinica, 30, 361-367, (2007) · Zbl 1141.60309
[10]	Wu, T-J; Shi, X; Miao, B, Asymptotic approximation of inverse moments of nonnegative random variables, Statistics & Probability Letters, 79, 1366-1371, (2009) · Zbl 1168.60340
[11]	Wang, X; Hu, S; Yang, W; Ling, N, Exponential inequalities and inverse moment for NOD sequence, Statistics and Probability Letters, 80, 452-461, (2010) · Zbl 1186.60015
[12]	Rosenthal, HP, On the subspaces of [inlineequation not available: see fulltext.] spanned by sequences of independent random variables, Israel Journal of Mathematics, 8, 273-303, (1970) · Zbl 0213.19303
[13]	Asadian, N; Fakoor, V; Bozorgnia, A, Rosenthal’s type inequalities for negatively orthant dependent random variables, Journal of the Iranian Statistical Society, 5, 69-75, (2006) · Zbl 1490.60044
[14]	Shao, QM, A moment inequality and its applications, Acta Mathematica Sinica, 31, 736-747, (1988) · Zbl 0698.60025
[15]	Shao, QM, Maximal inequalities for partial sums of [inlineequation not available: see fulltext.]-mixing sequences, The Annals of Probability, 23, 948-965, (1995) · Zbl 0831.60028
[16]	Shao, Q-M, A comparison theorem on moment inequalities between negatively associated and independent random variables, Journal of Theoretical Probability, 13, 343-356, (2000) · Zbl 0971.60015
[17]	Utev, S; Peligrad, M, Maximal inequalities and an invariance principle for a class of weakly dependent random variables, Journal of Theoretical Probability, 16, 101-115, (2003) · Zbl 1012.60022