An estimate on the supremum of a nice class of stochastic integrals and U-statistics

Probability Theory and Related Fields

Volumn 134, Issue 3, 2006, Pages 489-537

  Major, Péter ^a  

^a INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

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[No Author keywords available]

Indexed keywords

EID: 33749679752     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-005-0440-9     Document Type: Article

References (12)

1. Alexander, K.: The central limit theorem for empirical processes over Vapnik-Červonenkis classes. Ann. Probab. 15, 178-203 (1987)
2. Arcones, M. A., Giné, E.: Limit theorems for U-processes. Ann. Probab. 21, 1494-1542 (1993)
3. Arcones, M. A., Giné, E.: U-processes indexed by Vapnik-Červonenkis classes of functions with application to asymptotics and bootstrap of U-statistics with estimated parameters. Stoch. Proc. Appl. 52, 17-38 (1994)
4. Beckner, W.: Inequalities in Fourier Analysis. Ann. Math. 102, 159-182 (1975)
5. de la Peña, V. H., Giné, E.: Decoupling From dependence to independence. Springer series in statistics. Probability and its application. Springer Verlag, New York, Berlin, Heidelberg, 1999
6. de la Peña, V. H., Montgomery-Smith, S.: Decoupling inequalities for the tail-probabilities of multivariate U-statistics. Ann. Probab. 25, 806-816 (1995)
7. Giné, E., Zinn, J.: Some limit theorems for empirical processes. Ann. Probab. 12, 929-989 (1984)
8. Major, P.: On the tail behaviour of multiple random integrals and degenerate U-statistics. (manuscript for a future Lecture Note) 2004
9. Major, P.: A multivariate generalization of Hoeffding's inequality. Submitted to Ann. Probab. 2005
10. Major, P., Rejto, L.: Strong embedding of the distribution function under random censorship. Ann. Statis 16, 1113-1132 (1988)
11. Major, P. and Rejto, L.: A note on nonparametric estimations. In the conference volume to the 65. birthday of Miklós Csörgo 759-774 (1998)
12. Pollard, D.: Convergence of Stochastic Processes. Springer-Verlag, New York, 1984