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Bounds on the tail probability of $ U$-statistics and quadratic forms

Authors: Victor H. de la Peña and S. J. Montgomery-Smith
Journal: Bull. Amer. Math. Soc. 31 (1994), 223-227
MSC: Primary 60E15
MathSciNet review: 1261237
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  • [1] M. Arcones and E. Giné, Limit theorems for U-processes, Ann. Probab. 21 (1993), 1495-1592. MR 1235426 (94g:60060)
  • [2] J. Bourgain and L. Tzafriri, Invertibility of "large" submatrices with applications to the geometry of Banach spaces and harmonic analysis, Israel J. Math. 57 (1987), 137-224. MR 890420 (89a:46035)
  • [3] D. Burkholder, A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions, Conference on Harmonic Analysis in Honor of A. Zygmund (W. Beckner, A.P. Calderon, R. Fefferman, and P. Jones, eds.), Wadsworth, Belmont, CA, 1983, pp. 270-286. MR 730072 (85i:42020)
  • [4] V.H. de la Peña, Decoupling and Khintchine's inequalities for U-statistics, Ann. Probab. 20 (1992), 1877-1892. MR 1188046 (93j:60019)
  • [5] -, Nuevas desigualdades para U-estadísticas y gráficas aleatorias, Proceedings of the Fourth Latin American Congress of Probability and Math. Stat. (CLAPEM), México City, September 1990, 1992.
  • [6] V.H. de la Peña, S.J. Montgomery-Smith, and J. Szulga, Contraction and decoupling inequalities for multilinear forms and U-statistics, Ann. Probab. (to appear). MR 1331202 (96b:60009)
  • [7] E. Giné and J. Zinn, A remark on convergence in distribution of U-statistics, Ann. Probab. (to appear). MR 1258868 (94j:60035)
  • [8] S. Janson and K. Nowicki, The asymptotic distributions of generalized U-statistics with applications to random graphs, Probab. Theory Related Fields 90 (1991), 341-375. MR 1133371 (93b:62021)
  • [9] S. Kwapien and J. Szulga, Hypercontraction methods in moment inequalities for series of independent random variables in normed spaces, Ann. Probab. 19 (1991), 369-379. MR 1085342 (92a:60051)
  • [10] S. Kwapien and W. Woyczynski, Random series and stochastic integrals: Simple and multiple, Birkhäuser, New York, 1992.
  • [11] T.R. McConnell and M.S. Taqqu, Decoupling inequalities for multilinear forms in independent symmetric random variables, Ann. Probab. 14 (1986), 943-954. MR 841595 (87k:60053)
  • [12] D. Nolan and D. Pollard, U-processes: Rates of convergence, Ann. Statist. 15 (1987), 780-799. MR 888439 (88h:60062)

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Keywords: U-statistics, quadratic forms, decoupling
Article copyright: © Copyright 1994 American Mathematical Society

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