×

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

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
PDFBibTeX XMLCite
Full Text: DOI EuDML

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 1985, 47(2):362-371. · Zbl 0603.62016
[2] Pittenger AO: Sharp mean-variance bounds for Jensen-type inequalities. Statistics & Probability Letters 1990, 10(2):91-94. 10.1016/0167-7152(90)90001-N · Zbl 0705.60017 · doi:10.1016/0167-7152(90)90001-N
[3] Marciniak E, Wesołowski J: Asymptotic Eulerian expansions for binomial and negative binomial reciprocals. Proceedings of the American Mathematical Society 1999, 127(11):3329-3338. 10.1090/S0002-9939-99-05105-9 · Zbl 0930.60004 · doi:10.1090/S0002-9939-99-05105-9
[4] Fujioka T: Asymptotic approximations of the inverse moment of the noncentral chi-squared variable. Journal of the Japan Statistical Society 2001, 31(1):99-109. · Zbl 1031.62011 · doi:10.14490/jjss1995.31.99
[5] Jurlewicz A, Weron K: Relaxation of dynamically correlated clusters. Journal of Non-Crystalline Solids 2002, 305(1-3):112-121. · doi:10.1016/S0022-3093(02)01087-6
[6] Ramsay CM: A note on random survivorship group benefits. ASTIN Bulletin 1993, 23: 149-156. 10.2143/AST.23.1.2005106 · doi:10.2143/AST.23.1.2005106
[7] Garcia NL, Palacios JL: On inverse moments of nonnegative random variables. Statistics & Probability Letters 2001, 53(3):235-239. 10.1016/S0167-7152(01)00008-6 · Zbl 0991.60003 · doi:10.1016/S0167-7152(01)00008-6
[8] Kaluszka M, Okolewski A: On Fatou-type lemma for monotone moments of weakly convergent random variables. Statistics & Probability Letters 2004, 66(1):45-50. 10.1016/j.spl.2003.10.009 · Zbl 1116.60308 · doi:10.1016/j.spl.2003.10.009
[9] Hu SH, Chen GJ, Wang XJ, Chen EB: On inverse moments of nonnegative weakly convergent random variables. Acta Mathematicae Applicatae Sinica 2007, 30(2):361-367. · Zbl 1141.60309
[10] Wu T-J, Shi X, Miao B: Asymptotic approximation of inverse moments of nonnegative random variables. Statistics & Probability Letters 2009, 79(11):1366-1371. 10.1016/j.spl.2009.02.010 · Zbl 1168.60340 · doi:10.1016/j.spl.2009.02.010
[11] Wang X, Hu S, Yang W, Ling N: Exponential inequalities and inverse moment for NOD sequence. Statistics and Probability Letters 2010, 80(5-6):452-461. 10.1016/j.spl.2009.11.023 · Zbl 1186.60015 · doi:10.1016/j.spl.2009.11.023
[12] Rosenthal HP: On the subspaces of spanned by sequences of independent random variables. Israel Journal of Mathematics 1970, 8: 273-303. 10.1007/BF02771562 · Zbl 0213.19303 · doi:10.1007/BF02771562
[13] Asadian N, Fakoor V, Bozorgnia A: Rosenthal’s type inequalities for negatively orthant dependent random variables. Journal of the Iranian Statistical Society 2006, 5: 69-75. · Zbl 1490.60044
[14] Shao QM: A moment inequality and its applications. Acta Mathematica Sinica 1988, 31(6):736-747. · Zbl 0698.60025
[15] Shao QM: Maximal inequalities for partial sums of -mixing sequences. The Annals of Probability 1995, 23(2):948-965. 10.1214/aop/1176988297 · Zbl 0831.60028 · doi:10.1214/aop/1176988297
[16] Shao Q-M: A comparison theorem on moment inequalities between negatively associated and independent random variables. Journal of Theoretical Probability 2000, 13(2):343-356. 10.1023/A:1007849609234 · Zbl 0971.60015 · doi:10.1023/A:1007849609234
[17] Utev S, Peligrad M: Maximal inequalities and an invariance principle for a class of weakly dependent random variables. Journal of Theoretical Probability 2003, 16(1):101-115. 10.1023/A:1022278404634 · Zbl 1012.60022 · doi:10.1023/A:1022278404634
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.