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Bounds on the tail probability of U-statistics and quadratic forms
Author(s):
Victor
H.
de la Pe\~na;
S.
J.
Montgomery-Smith
Journal:
Bull. Amer. Math. Soc.
31
(1994),
223-227.
MSC (1991):
Primary 60E15;
Secondary 60D05, 60E05
MathSciNet review:
1261237
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References |
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Additional information
References:
- [1]
- M.~Arcones and E.~Gin\'e, Limit theorems for U-processes, Ann. Probab. \textbf{21} (1993), 1495--1592. MR 1235426
- [2]
- J.~Bourgain and L.~Tzafriri, Invertibility of\, \RM {``}large\RM {''} submatrices with applications to the geometry of Banach spaces and harmonic analysis, Israel J. Math. \textbf{57} (1987), 137--224. MR 890420
- [3]
- D.~Burkholder, \emph{A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions}, Wadsworth, Belmont, CA, 1983 pp.~270--286. MR 730072
- [4]
- V.H.~de~la~Pe\~na, Decoupling and Khintchine\RM 's inequalities for U-statistics, Ann. Probab. \textbf{20} (1992), 1877--1892. MR 1188046
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- V.H.~de~la~Pe\~na, \emph{Nuevas desigualdades para U-estad\'isticas y gr\'aficas aleatorias}, 1992. MR
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- V.H.~de~la~Pe\~na, S.J.~Montgomery-Smith, and J.~Szulga, Contraction and decoupling inequalities for multilinear forms and U-statistics, Ann. Probab. MR
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- E.~Gin\'e and J.~Zinn, A remark on convergence in distribution of U-statistics, Ann. Probab. (to appear). MR 1258868
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- S.~Janson and K.~Nowicki, The asymptotic distributions of generalized U-statistics with applications to random graphs, Probab. Theory Related Fields \textbf{90} (1991), 341--375. MR 1133371
- [9]
- S.~Kwapien and J.~Szulga, Hypercontraction methods in moment inequalities for series of independent random variables in normed spaces, Ann. Probab. \textbf{19} (1991), 369--379. MR 1085342
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- S.~Kwapien and W.~Woyczynski, Random series and stochastic integrals\,\RM : Simple and multiple, Birkh\"auser, New York, 1992. MR 1167198
- [11]
- T.R.~McConnell and M.S.~Taqqu, Decoupling inequalities for multilinear forms in independent symmetric random variables, Ann. Probab. \textbf{14} (1986), 943--954. MR 841595
- [12]
- D.~Nolan and D.~Pollard, U-processes\,\RM : Rates of convergence, Ann. Statist. \textbf{15} (1987), 780--799. MR 888439
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Additional Information:
DOI:
10.1090/S0273-0979-1994-00522-1
PII:
S 0273-0979(1994)00522-1
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