Exact rates in Vapnik-Chervonenkis bounds
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 1, pp. 95-119. 
@article{AIHPB_2003__39_1_95_0,
     author = {Vayatis, Nicolas},
     title = {Exact rates in {Vapnik-Chervonenkis} bounds},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {95--119},
     publisher = {Elsevier},
     volume = {39},
     number = {1},
     year = {2003},
     zbl = {1020.60010},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2003__39_1_95_0/}
}
TY  - JOUR
AU  - Vayatis, Nicolas
TI  - Exact rates in Vapnik-Chervonenkis bounds
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2003
SP  - 95
EP  - 119
VL  - 39
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/item/AIHPB_2003__39_1_95_0/
LA  - en
ID  - AIHPB_2003__39_1_95_0
ER  - 
%0 Journal Article
%A Vayatis, Nicolas
%T Exact rates in Vapnik-Chervonenkis bounds
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2003
%P 95-119
%V 39
%N 1
%I Elsevier
%U http://www.numdam.org/item/AIHPB_2003__39_1_95_0/
%G en
%F AIHPB_2003__39_1_95_0
Vayatis, Nicolas. Exact rates in Vapnik-Chervonenkis bounds. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 1, pp. 95-119. http://www.numdam.org/item/AIHPB_2003__39_1_95_0/

[1] K. Alexander, Probability inequalities for empirical processes and a law of the iterated logarithm, Ann. Probab. 4 (1984) 1041-1067. | MR | Zbl

[2] R. Azencott, Communication for the fifty years of the Department of Mathematics at Brown University (USA), 1996.

[3] S. Boucheron, G. Lugosi, P. Massart, A sharp concentration inequality with applications, Random Structures and Algorithms 16 (3) (2000) 277-292. | MR | Zbl

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

[5] L. Devroye, Bounds for the uniform deviation of empirical measures, J. Multivariate Anal. 12 (1982) 72-79. | MR | Zbl

[6] L. Devroye, L. Györfi, G. Lugosi, A Probabilistic Theory of Pattern Recognition, Springer, 1996. | MR | Zbl

[7] R.M. Dudley, A course on empirical processes, in: Hennequin P.L. (Ed.), Ecole d'Eté de Probabilités de Saint-Flour XII - 1982, Lecture Notes in Mathematics, 1097, Springer-Verlag, 1982, pp. 1-142. | MR | Zbl

[8] A. Dvoretzky, J. Kiefer, J. Wolfowitz, Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator, Ann. Math. Statist. 27 (1956) 642-669. | MR | Zbl

[9] E. Giné, J. Zinn, On the central limit theorem for empirical processes, Ann. Probab. 12 (1984) 929-989. | MR | Zbl

[10] D. Haussler, Sphere packing numbers for subsets of the Boolean n-cube with bounded Vapnik-Chervonenkis dimension, J. Combin. Theory Series A 69 (1995) 217-232. | Zbl

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

[12] J. Kiefer, On large deviations of the empirical d.f. of vector chance variables and a law of the iterated logarithm, Pacific J. Math. 11 (1961) 649-660. | MR | Zbl

[13] M. Ledoux, M. Talagrand, Probability in Banach Spaces, Springer-Verlag, 1992. | MR | Zbl

[14] G. Lugosi, Improved upper bounds for probabilities of uniform deviations, Statist. Probab. Lett. 25 (1995) 71-77. | MR | Zbl

[15] P. Massart, Rates of convergence in the central limit theorem for empirical processes, Annales de l'Institut Henri Poincaré 22 (4) (1986) 381-423. | Numdam | MR | Zbl

[16] P. Massart, The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality, Ann. Probab. 18 (1990) 1269-1283. | Zbl

[17] J.M.R. Parrondo, C. Van Den Broeck, Vapnik-Chervonenkis bounds for generalization, J. Phys. A: Math. Gen. 26 (1993) 2211-2223. | Zbl

[18] D. Pollard, Convergence of Stochastic Processes, Springer-Verlag, 1984. | MR | Zbl

[19] D. Pollard, Empirical Processes: Theory and Applications, NSF-CBMS Regional Conference Series in Probability and Statistics, 2, Institute of Mathematical Statistics, 1991. | MR | Zbl

[20] E. Rio, Inégalités de concentration pour les processus empiriques de classes de parties, Probab. Theory Related Fields (2000), to appear. | MR | Zbl

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

[22] A.W. Van Der Vaart, J.A. Wellner, Weak Convergence and Empirical Processes, Springer, 1996. | MR | Zbl

[23] V.N. Vapnik, Estimation of Dependencies on the Basis of Empirical Data, Springer, 1982.

[24] V.N. Vapnik, The Nature of Statistical Learning Theory, Springer, 1995. | MR | Zbl

[25] V.N. Vapnik, Statistical Learning Theory, Wiley-Interscience, 1998. | MR | Zbl

[26] V.N. Vapnik, A.Y. Chervonenkis, On the uniform convergence of relative frequencies of events to their probabilities, Theory Probab. Appl. 16 (1971) 264-280. | Zbl

[27] V.N. Vapnik, A.Y. Chervonenkis, Necessary and sufficient conditions for the uniform convergence of the means to their expectations, Theory Probab. Appl. 26 (1981) 532-555. | MR | Zbl

[28] V.N. Vapnik, E. Levin, Y. Le Cun, Measuring the VC-dimension of a learning machine, Neural Comput. 6 (1994) 851-876.

[29] N. Vayatis, Inégalités de Vapnik-Chervonenkis et mesures de complexité, Ph.D. thesis, Ecole Polytechnique, 2000, in English.

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