Moderate deviations for functional U-processes
Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 2, pp. 245-273. 
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     author = {Eichelsbacher, Peter},
     title = {Moderate deviations for functional $U$-processes},
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     pages = {245--273},
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     number = {2},
     year = {2001},
     zbl = {0987.60033},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2001__37_2_245_0/}
}
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Eichelsbacher, Peter. Moderate deviations for functional $U$-processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 2, pp. 245-273. http://www.numdam.org/item/AIHPB_2001__37_2_245_0/

[1] M.A Arcones, E Giné, Limit theorems for U-processes, Ann. Probab. 21 (1993) 1494-1542. | MR | Zbl

[2] M.A Arcones, E Giné, 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 | Zbl

[3] M.A Arcones, E Giné, On the law of the iterated logarithm for canonical U-statistics and processes, Stochastic Process. Appl. 58 (1995) 217-245. | MR | Zbl

[4] P Baldi, Large deviations and stochastic homogenization, Ann. Mat. Pura Appl. 151 (1988) 161-177. | MR | Zbl

[5] A.A Borovkov, A.A Mogulskii, Probabilities of large deviations in topological spaces I, Siberian Math. J. 19 (1978) 697-709. | MR | Zbl

[6] A.A Borovkov, A.A Mogulskii, Probabilities of large deviations in topological spaces II, Siberian Math. J. 21 (1980) 653-664. | MR | Zbl

[7] Yu.V Borovskikh, U-Statistics in Banach Spaces, VSP, Utrecht, 1996. | MR | Zbl

[8] A Dembo, T Zajic, Uniform large and moderate deviations for functional empirical processes, Stochastic Process. Appl. 67 (1997) 195-211. | MR | Zbl

[9] A Dembo, O Zeitouni, Large Deviations Techniques and Applications, Springer, New York, 1998. | MR | Zbl

[10] R.M Dudley, A course on empirical processes, in: Dold A, Eckmann B (Eds.), École d'Eté de Probabilités de Saint-Flour XII, Lecture Notes in Math., 1097, Springer, New York, 1984, pp. 1-142. | MR | Zbl

[11] P Eichelsbacher, Large deviations for products of empirical probability measures in the τ-topology, J. Theoret. Probab. 10 (4) (1997) 903-920. | Zbl

[12] P Eichelsbacher, M Löwe, Large deviations for partial sums U-processes, Theory Probab. Appl. 43 (1998) 97-115. | MR | Zbl

[13] P Eichelsbacher, U Schmock, Exponential approximations in completely regular topological spaces and extensions of Sanov's theorem, Stochastic Process. Appl. 77 (2) (1998) 233-251. | MR | Zbl

[14] P Eichelsbacher, U Schmock, Large and rank-dependent moderate deviations for U-empirical measures in strong topologies, preprint, 1998. | MR

[15] E Giné, V De La Peña, Decoupling: From Dependence to Independence, Springer-Verlag, 1999. | MR | Zbl

[16] E Giné, C.-H Zhang, On integrability in the LIL for degenerate U-statistics, J. Theoret. Probab. 9 (2) (1996) 385-412. | MR | Zbl

[17] P Hall, On the invariance principle for U-statistics, Stochastic Process. Appl. 9 (1979) 163-174. | MR | Zbl

[18] W Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc. 58 (1963) 13-30. | MR | Zbl

[19] M Ledoux, M Talagrand, Probability in Banach Spaces, Springer-Verlag, Berlin, 1991. | MR | Zbl

[20] A Mandelbaum, M.S Taqqu, Invariance principle for symmetric statistics, Ann. Statist. 12 (1984) 483-496. | MR | Zbl

[21] R.G Miller, P.K Sen, Weak convergence of U-statistics and von Mises differentiable, Ann. Math. Statist. 43 (1972) 31-41. | MR | Zbl

[22] A.A Mogulskii, Large deviations for trajectories of multidimensional random walks, Theory Probab. Appl. 21 (1976) 300-315. | MR | Zbl

[23] S.J Montgomery-Smith, Comparison of sums of independent identically distributed random vectors, Probab. Math. Statist. 14 (2) (1994) 281-285. | MR | Zbl

[24] S.J Montgomery-Smith, V De La Peña, Decoupling inequalities for the tail probabilities of multivariate U-statistics, Ann. Probab. 23 (2) (1995) 806-816. | MR | Zbl

[25] D Pollard, Convergence of Stochastic Processes, Springer, New York, 1984. | MR | Zbl

[26] M Talagrand, Sharper bounds for gaussian and empirical processes, Ann. Probab. 22 (1) (1994) 28-76. | MR | Zbl

[27] L Wu, Large deviations, moderate deviations and LIL for empirical processes, Ann. Probab. 22 (1) (1994) 17-27. | MR | Zbl

[28] V.V Yurinsky, Exponential inequalities for sums of random vectors, J. Mult. Anal. 6 (4) (1976) 473-499. | MR | Zbl

[29] V.V Yurinsky, Sums and Gaussian Vectors, Lecture Notes in Mathematics, 1617, Springer-Verlag, Berlin, 1995. | MR | Zbl