Laplace transform estimates and deviation inequalities
Catoni, Olivier
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003), p. 1-26 / Harvested from Numdam
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Publié le : 2003-01-01
@article{AIHPB_2003__39_1_1_0,
     author = {Catoni, Olivier},
     title = {Laplace transform estimates and deviation inequalities},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {39},
     year = {2003},
     pages = {1-26},
     mrnumber = {1959840},
     zbl = {1012.60023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2003__39_1_1_0}
}

Catoni, Olivier. Laplace transform estimates and deviation inequalities. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) pp. 1-26. http://gdmltest.u-ga.fr/item/AIHPB_2003__39_1_1_0/

[1] K. Azuma, Weighted sums of certain dependent random variables, Tôhoku Math. J. (2) 19 (1967) 357-367. | MR 221571 | Zbl 0178.21103

[2] S. Boucheron, G. Lugosi, P. Massart, A sharp concentration inequality with applications, Prépublication d'Orsay numéro 25 (27/9/1999), http://www.math.u-psud.fr/~biblio/html/ppo.html. | MR 1749290

[3] O. Catoni, “Universal” aggregation rules with exact bias bounds, preprint PMA-510, http://www.proba.jussieu.fr/mathdoc/preprints/index.html#1999.

[4] O. Catoni, Gibbs estimators, preprint LMENS-98-21, 1998, http://www.dmi.ens.fr/preprints/.

[5] A. Dembo, O. Zeitouni, Transportation approach to some concentration inequalities in product spaces, Electron. Comm. Probab. 1 (9) (1996) 83-90, (electronic). | MR 1423908 | Zbl 0916.28003

[6] W. Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc. 58 (1963) 13-30. | MR 144363 | Zbl 0127.10602

[7] M. Ledoux, Concentration of measure and logarithmic Sobolev inequalities, Notes Berlin, 1997. | Numdam | Zbl 0957.60016

[8] M. Ledoux, On Talagrand's deviation inequalities for product measures, ESAIM Probab. Statist. 1 (1995) 63-87. | Numdam | MR 1399224 | Zbl 0869.60013

[9] M. Ledoux, Isoperimetry and Gaussian analysis, in: Lectures on Probability Theory and Statistics (Saint-Flour, 1994), Lecture Notes in Math., 1648, Springer, Berlin, 1996, pp. 165-294. | MR 1600888 | Zbl 0874.60005

[10] M. Ledoux, M. Talagrand, Probability in Banach Spaces, Springer, Berlin, 1991. | MR 1102015 | Zbl 0748.60004

[11] K. Marton, Measure concentration for a class of random processes, Probab. Theory Related Fields 110 (3) (1998) 427-439. | MR 1616492 | Zbl 0927.60050

[12] K. Marton, A measure concentration inequality for contracting Markov chains, Geom. Funct. Anal. 6 (3) (1996) 556-571. | MR 1392329 | Zbl 0856.60072

[13] K. Marton, Bounding d ¯-distance by informational divergence: a method to prove measure concentration, Ann. Probab. 24 (2) (1996) 857-866. | MR 1404531 | Zbl 0865.60017

[14] P. Massart, About the constants in Talagrand's concentration inequalities for empirical processes, Ann. Probab., 1999, to appear. | MR 1782276 | Zbl 1140.60310 | Zbl 01905939

[15] P. Massart, Optimal constants for Hoeffding type inequalities, Prépublication d'Orsay numéro 86 (18/12/1998), http://www.math.u-psud.fr/~biblio/html/ppo.html.

[16] C. Mcdiarmid, Concentration, in: Habib M., Mcdiarmid C., Reed B. (Eds.), Probabilistic Methods for Algorithmic Discrete Mathematics, Springer, 1998. | MR 1678554 | Zbl 0927.60027

[17] K.R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967. | MR 226684 | Zbl 0153.19101

[18] P.-M. Samson, Concentration of measure inequalities for Markov chains and Φ-mixing processes, Ann. Probab., 1998, to appear. | Zbl 1044.60061

[19] P.-M. Samson, Inégalités de concentration de la mesure pour des chaînes de Markov et des processus Φ-mélangeants, PhD, Université Paul Sabatier, Toulouse, France, June 1998.

[20] M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Publ. Math. IHES 81 (1995) 73-205. | Numdam | MR 1361756 | Zbl 0864.60013

[21] V.V. Yurinskiĭ, Exponential estimates for large deviations, Teor. Verojatnost. i Primenen. 19 (1974) 152-154, (Russian). | MR 334298 | Zbl 0323.60029