@article{AIHPB_2001__37_2_245_0,
author = {Eichelsbacher, Peter},
title = {Moderate deviations for functional $U$-processes},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
volume = {37},
year = {2001},
pages = {245-273},
zbl = {0987.60033},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPB_2001__37_2_245_0}
}
Eichelsbacher, Peter. Moderate deviations for functional $U$-processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) pp. 245-273. http://gdmltest.u-ga.fr/item/AIHPB_2001__37_2_245_0/
[1] , , Limit theorems for U-processes, Ann. Probab. 21 (1993) 1494-1542. | MR 1235426 | Zbl 0789.60031
[2] , , U-processes indexed by Vapnik-Červonenkis classes of functions with applications to asymptotics and bootstrap of U-statistics with estimated parameters, Stochastic Process. Appl. 52 (1994) 17-38. | MR 1289166 | Zbl 0807.62014
[3] , , On the law of the iterated logarithm for canonical U-statistics and processes, Stochastic Process. Appl. 58 (1995) 217-245. | MR 1348376 | Zbl 0829.60003
[4] , Large deviations and stochastic homogenization, Ann. Mat. Pura Appl. 151 (1988) 161-177. | MR 964508 | Zbl 0654.60024
[5] , , Probabilities of large deviations in topological spaces I, Siberian Math. J. 19 (1978) 697-709. | MR 508496 | Zbl 0413.60021
[6] , , Probabilities of large deviations in topological spaces II, Siberian Math. J. 21 (1980) 653-664. | MR 592213 | Zbl 0458.60019
[7] , U-Statistics in Banach Spaces, VSP, Utrecht, 1996. | MR 1419498 | Zbl 0865.60004
[8] , , Uniform large and moderate deviations for functional empirical processes, Stochastic Process. Appl. 67 (1997) 195-211. | MR 1449831 | Zbl 0890.60022
[9] , , Large Deviations Techniques and Applications, Springer, New York, 1998. | MR 1619036 | Zbl 0896.60013
[10] , A course on empirical processes, in: , (Eds.), École d'Eté de Probabilités de Saint-Flour XII, Lecture Notes in Math., 1097, Springer, New York, 1984, pp. 1-142. | MR 876079 | Zbl 0554.60029
[11] , Large deviations for products of empirical probability measures in the τ-topology, J. Theoret. Probab. 10 (4) (1997) 903-920. | Zbl 0891.60031
[12] , , Large deviations for partial sums U-processes, Theory Probab. Appl. 43 (1998) 97-115. | MR 1669988 | Zbl 0927.60047
[13] , , Exponential approximations in completely regular topological spaces and extensions of Sanov's theorem, Stochastic Process. Appl. 77 (2) (1998) 233-251. | MR 1649006 | Zbl 0934.60023
[14] , , Large and rank-dependent moderate deviations for U-empirical measures in strong topologies, preprint, 1998. | MR 1981633
[15] , , Decoupling: From Dependence to Independence, Springer-Verlag, 1999. | MR 1666908 | Zbl 0918.60021
[16] , , On integrability in the LIL for degenerate U-statistics, J. Theoret. Probab. 9 (2) (1996) 385-412. | MR 1385404 | Zbl 0873.60015
[17] , On the invariance principle for U-statistics, Stochastic Process. Appl. 9 (1979) 163-174. | MR 548836 | Zbl 0422.62019
[18] , Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc. 58 (1963) 13-30. | MR 144363 | Zbl 0127.10602
[19] , , Probability in Banach Spaces, Springer-Verlag, Berlin, 1991. | MR 1102015 | Zbl 0748.60004
[20] , , Invariance principle for symmetric statistics, Ann. Statist. 12 (1984) 483-496. | MR 740907 | Zbl 0547.60039
[21] , , Weak convergence of U-statistics and von Mises differentiable, Ann. Math. Statist. 43 (1972) 31-41. | MR 300321 | Zbl 0238.62057
[22] , Large deviations for trajectories of multidimensional random walks, Theory Probab. Appl. 21 (1976) 300-315. | MR 420798 | Zbl 0366.60031
[23] , Comparison of sums of independent identically distributed random vectors, Probab. Math. Statist. 14 (2) (1994) 281-285. | MR 1321767 | Zbl 0827.60005
[24] , , Decoupling inequalities for the tail probabilities of multivariate U-statistics, Ann. Probab. 23 (2) (1995) 806-816. | MR 1334173 | Zbl 0827.60014
[25] , Convergence of Stochastic Processes, Springer, New York, 1984. | MR 762984 | Zbl 0544.60045
[26] , Sharper bounds for gaussian and empirical processes, Ann. Probab. 22 (1) (1994) 28-76. | MR 1258865 | Zbl 0798.60051
[27] , Large deviations, moderate deviations and LIL for empirical processes, Ann. Probab. 22 (1) (1994) 17-27. | MR 1258864 | Zbl 0793.60032
[28] , Exponential inequalities for sums of random vectors, J. Mult. Anal. 6 (4) (1976) 473-499. | MR 428401 | Zbl 0346.60001
[29] , Sums and Gaussian Vectors, Lecture Notes in Mathematics, 1617, Springer-Verlag, Berlin, 1995. | MR 1442713 | Zbl 0846.60003