Bounds on the tail probability of $U$-statistics and quadratic forms
HTML articles powered by AMS MathViewer
- by Victor H. de la Peña and S. J. Montgomery-Smith PDF
- Bull. Amer. Math. Soc. 31 (1994), 223-227 Request permission
References
- Miguel A. Arcones and Evarist Giné, Limit theorems for $U$-processes, Ann. Probab. 21 (1993), no. 3, 1494–1542. MR 1235426
- 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), no. 2, 137–224. MR 890420, DOI 10.1007/BF02772174
- D. L. Burkholder, A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions, Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981) Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 270–286. MR 730072
- Victor H. de la Peña, Decoupling and Khintchine’s inequalities for $U$-statistics, Ann. Probab. 20 (1992), no. 4, 1877–1892. MR 1188046 —, 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.
- V. H. de la Peña, S. J. Montgomery-Smith, and Jerzy Szulga, Contraction and decoupling inequalities for multilinear forms and $U$-statistics, Ann. Probab. 22 (1994), no. 4, 1745–1765. MR 1331202, DOI 10.1214/aop/1176988481
- Evarist Giné and Joel Zinn, A remark on convergence in distribution of $U$-statistics, Ann. Probab. 22 (1994), no. 1, 117–125. MR 1258868
- Svante Janson and Krzysztof Nowicki, The asymptotic distributions of generalized $U$-statistics with applications to random graphs, Probab. Theory Related Fields 90 (1991), no. 3, 341–375. MR 1133371, DOI 10.1007/BF01193750
- Stanisław Kwapień and Jerzy Szulga, Hypercontraction methods in moment inequalities for series of independent random variables in normed spaces, Ann. Probab. 19 (1991), no. 1, 369–379. MR 1085342 S. Kwapien and W. Woyczynski, Random series and stochastic integrals: Simple and multiple, Birkhäuser, New York, 1992.
- Terry R. McConnell and Murad S. Taqqu, Decoupling inequalities for multilinear forms in independent symmetric random variables, Ann. Probab. 14 (1986), no. 3, 943–954. MR 841595
- Deborah Nolan and David Pollard, $U$-processes: rates of convergence, Ann. Statist. 15 (1987), no. 2, 780–799. MR 888439, DOI 10.1214/aos/1176350374
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 31 (1994), 223-227
- MSC: Primary 60E15
- DOI: https://doi.org/10.1090/S0273-0979-1994-00522-1
- MathSciNet review: 1261237