On sharp Burkholder–Rosenthal-type inequalities for infinite-degree U-statistics

Victor H. de La Peña; Rustam Ibragimov; Shaturgun Sharakhmetov

Annales de l'I.H.P. Probabilités et statistiques (2002)

  • Volume: 38, Issue: 6, page 973-990
  • ISSN: 0246-0203

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de La Peña, Victor H., Ibragimov, Rustam, and Sharakhmetov, Shaturgun. "On sharp Burkholder–Rosenthal-type inequalities for infinite-degree U-statistics." Annales de l'I.H.P. Probabilités et statistiques 38.6 (2002): 973-990. <http://eudml.org/doc/77751>.

@article{deLaPeña2002,
author = {de La Peña, Victor H., Ibragimov, Rustam, Sharakhmetov, Shaturgun},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {infinite degree U-statistics; decoupling inequalities; Burkholder-Rosenthal inequalities},
language = {eng},
number = {6},
pages = {973-990},
publisher = {Elsevier},
title = {On sharp Burkholder–Rosenthal-type inequalities for infinite-degree U-statistics},
url = {http://eudml.org/doc/77751},
volume = {38},
year = {2002},
}

TY - JOUR
AU - de La Peña, Victor H.
AU - Ibragimov, Rustam
AU - Sharakhmetov, Shaturgun
TI - On sharp Burkholder–Rosenthal-type inequalities for infinite-degree U-statistics
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 6
SP - 973
EP - 990
LA - eng
KW - infinite degree U-statistics; decoupling inequalities; Burkholder-Rosenthal inequalities
UR - http://eudml.org/doc/77751
ER -

References

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  1. [1] V.H. de la Peña, Decoupling and Khintchine's inequalities for U-statistics, Ann. Probab.20 (1992) 1877-1892. Zbl0761.60014MR1188046
  2. [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. Zbl1033.60019MR1964944
  3. [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. Zbl0969.60024
  4. [4] C. Heilig, D. Nolan, Limit theorems for the infinite-degree U-statistics, Statist. Sinica11 (2001) 289-302. Zbl1057.62518MR1820012
  5. [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. [6] R. Ibragimov, Sh. Sharakhmetov, Bounds on moments of symmetric statistics, Studia Sci. Math. Hungar. (1996), to appear. Zbl1064.60031MR1956938
  7. [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. Zbl1064.60031
  8. [8] R. Ibragimov, Sh. Sharakhmetov, Analogues of Khintchine, Marcinkiewicz–Zygmund and Rosenthal inequalities for symmetric statistics, Scand. J. Statist.26 (1999) 621-633. Zbl0944.60031
  9. [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. [10] R. Ibragimov, Sh. Sharakhmetov, A. Cecen, Exact estimates for moments of random bilinear forms, J. Theoret. Probab.14 (2001) 21-37. Zbl0979.60009MR1822892
  11. [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. Zbl0895.60018
  12. [12] S.A. Utev, Extremal problems in moment inequalities, Proc. Mathematical Institute of the Siberian Branch of the USSR Academy of Sciences5 (1985) 56-75, in Russian. Zbl0579.60018MR821753

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