On sharp Burkholder-Rosenthal-type inequalities for infinite-degree $U$-statistics
Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 6, p. 973-990
@article{AIHPB_2002__38_6_973_0,
author = {La Pe\~na, Victor H. de and Ibragimov, Rustam and Sharakhmetov, Shaturgun},
title = {On sharp Burkholder-Rosenthal-type inequalities for infinite-degree $U$-statistics},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
publisher = {Elsevier},
volume = {38},
number = {6},
year = {2002},
pages = {973-990},
zbl = {1016.60019},
language = {en},
url = {http://www.numdam.org/item/AIHPB_2002__38_6_973_0}
}

de La Peña, Victor H.; Ibragimov, Rustam; Sharakhmetov, Shaturgun. On sharp Burkholder-Rosenthal-type inequalities for infinite-degree $U$-statistics. Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 6, pp. 973-990. http://www.numdam.org/item/AIHPB_2002__38_6_973_0/

[1] V.H. De La Peña, Decoupling and Khintchine's inequalities for U-statistics, Ann. Probab. 20 (1992) 1877-1892. | MR 1188046 | Zbl 0761.60014

[2] V.H. De La Peña, R. Ibragimov, Sh. Sharakhmetov, On extremal distributions and sharp Lp-bounds for sums of multilinear forms, Ann. Probab. (2000), to appear. | MR 1964944 | Zbl 1033.60019

[3] E. Giné, R. Latała, J. Zinn, Exponential and moment inequalities for U-statistics, in: High Dimensional Probability II - Progress in Probability, Birkhauser, 2000, pp. 13-38. | Zbl 0969.60024

[4] C. Heilig, D. Nolan, Limit theorems for the infinite-degree U-statistics, Statist. Sinica 11 (2001) 289-302. | MR 1820012 | Zbl 1057.62518

[5] R. Ibragimov, Estimates for the moments of symmetric statistics, Ph.D. Dissertation, Institute of Mathematics of Uzbek Academy of Sciences, Tashkent, 1997, 127 pp. (in Russian).

[6] R. Ibragimov, Sh. Sharakhmetov, Bounds on moments of symmetric statistics, Studia Sci. Math. Hungar. (1996), to appear. | MR 1956938 | Zbl 1064.60031

[7] R. Ibragimov, Sh. Sharakhmetov, Exact bounds on the moments of symmetric statistics, in: 7th Vilnius Conference on Probability Theory and Mathematical Statistics/22nd European Meeting of Statisticians, Abstracts of communications, Vilnius, Lithuania, 1998, pp. 243-244.

[8] R. Ibragimov, Sh. Sharakhmetov, Analogues of Khintchine, Marcinkiewicz-Zygmund and Rosenthal inequalities for symmetric statistics, Scand. J. Statist. 26 (1999) 621-633. | Zbl 0944.60031

[9] R. Ibragimov, Sh. Sharakhmetov, Moment inequalities for symmetric statistics, in: Modern Problems of Probability Theory and Mathematical Statistics. Proceedings of the 4th Fergana International Colloquium on Probability Theory and Mathematical Statistics, 27-29 September, 1995, Tashkent, 2000, pp. 184-193, (in Russian), http://front.math.ucdavis.edu/math.PR/0005004.

[10] R. Ibragimov, Sh. Sharakhmetov, A. Cecen, Exact estimates for moments of random bilinear forms, J. Theoret. Probab. 14 (2001) 21-37. | MR 1822892 | Zbl 0979.60009

[11] M.J. Klass, K. Nowicki, Order of magnitude bounds for expectations of Δ2-functions of nonnegative random bilinear forms and generalized U-statistics, Ann. Probab. 25 (1997) 1471-1501. | Zbl 0895.60018

[12] S.A. Utev, Extremal problems in moment inequalities, Proc. Mathematical Institute of the Siberian Branch of the USSR Academy of Sciences 5 (1985) 56-75, in Russian. | MR 821753 | Zbl 0579.60018