Laplace transform estimates and deviation inequalities

Olivier Catoni

Annales de l'I.H.P. Probabilités et statistiques (2003)

  • Volume: 39, Issue: 1, page 1-26
  • ISSN: 0246-0203

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Catoni, Olivier. "Laplace transform estimates and deviation inequalities." Annales de l'I.H.P. Probabilités et statistiques 39.1 (2003): 1-26. <http://eudml.org/doc/77755>.

@article{Catoni2003,
author = {Catoni, Olivier},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {concentration of product measures; deviation inequalities; Markov chains; maximal coupling; central limit theorem},
language = {eng},
number = {1},
pages = {1-26},
publisher = {Elsevier},
title = {Laplace transform estimates and deviation inequalities},
url = {http://eudml.org/doc/77755},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Catoni, Olivier
TI - Laplace transform estimates and deviation inequalities
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2003
PB - Elsevier
VL - 39
IS - 1
SP - 1
EP - 26
LA - eng
KW - concentration of product measures; deviation inequalities; Markov chains; maximal coupling; central limit theorem
UR - http://eudml.org/doc/77755
ER -

References

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  1. [1] K. Azuma, Weighted sums of certain dependent random variables, Tôhoku Math. J. (2)19 (1967) 357-367. Zbl0178.21103MR221571
  2. [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. MR1749290
  3. [3] O. Catoni, “Universal” aggregation rules with exact bias bounds, preprint PMA-510, http://www.proba.jussieu.fr/mathdoc/preprints/index.html#1999. 
  4. [4] O. Catoni, Gibbs estimators, preprint LMENS-98-21, 1998, http://www.dmi.ens.fr/preprints/. 
  5. [5] A. Dembo, O. Zeitouni, Transportation approach to some concentration inequalities in product spaces, Electron. Comm. Probab.1 (9) (1996) 83-90, (electronic). Zbl0916.28003MR1423908
  6. [6] W. Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc.58 (1963) 13-30. Zbl0127.10602MR144363
  7. [7] M. Ledoux, Concentration of measure and logarithmic Sobolev inequalities, Notes Berlin, 1997. Zbl0957.60016
  8. [8] M. Ledoux, On Talagrand's deviation inequalities for product measures, ESAIM Probab. Statist.1 (1995) 63-87. Zbl0869.60013MR1399224
  9. [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. Zbl0874.60005MR1600888
  10. [10] M. Ledoux, M. Talagrand, Probability in Banach Spaces, Springer, Berlin, 1991. Zbl0748.60004MR1102015
  11. [11] K. Marton, Measure concentration for a class of random processes, Probab. Theory Related Fields110 (3) (1998) 427-439. Zbl0927.60050MR1616492
  12. [12] K. Marton, A measure concentration inequality for contracting Markov chains, Geom. Funct. Anal.6 (3) (1996) 556-571. Zbl0856.60072MR1392329
  13. [13] K. Marton, Bounding d ¯ -distance by informational divergence: a method to prove measure concentration, Ann. Probab.24 (2) (1996) 857-866. Zbl0865.60017MR1404531
  14. [14] P. Massart, About the constants in Talagrand's concentration inequalities for empirical processes, Ann. Probab., 1999, to appear. Zbl1140.60310MR1782276
  15. [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. [16] C. McDiarmid, Concentration, in: Habib M., McDiarmid C., Reed B. (Eds.), Probabilistic Methods for Algorithmic Discrete Mathematics, Springer, 1998. Zbl0927.60027MR1678554
  17. [17] K.R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967. Zbl0153.19101MR226684
  18. [18] P.-M. Samson, Concentration of measure inequalities for Markov chains and Φ-mixing processes, Ann. Probab., 1998, to appear. Zbl1044.60061
  19. [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. [20] M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Publ. Math. IHES81 (1995) 73-205. Zbl0864.60013MR1361756
  21. [21] V.V. Yurinskiĭ, Exponential estimates for large deviations, Teor. Verojatnost. i Primenen.19 (1974) 152-154, (Russian). Zbl0323.60029MR334298

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