@article{AFST_2000_6_9_2_245_0,
author = {Massart, Pascal},
title = {Some applications of concentration inequalities to statistics},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {245--303},
publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences},
address = {Toulouse},
volume = {Ser. 6, 9},
number = {2},
year = {2000},
mrnumber = {1813803},
zbl = {0986.62002},
language = {en},
url = {http://archive.numdam.org/item/AFST_2000_6_9_2_245_0/}
}
TY - JOUR AU - Massart, Pascal TI - Some applications of concentration inequalities to statistics JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2000 SP - 245 EP - 303 VL - 9 IS - 2 PB - Université Paul Sabatier. Faculté des sciences PP - Toulouse UR - http://archive.numdam.org/item/AFST_2000_6_9_2_245_0/ LA - en ID - AFST_2000_6_9_2_245_0 ER -
%0 Journal Article %A Massart, Pascal %T Some applications of concentration inequalities to statistics %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2000 %P 245-303 %V 9 %N 2 %I Université Paul Sabatier. Faculté des sciences %C Toulouse %U http://archive.numdam.org/item/AFST_2000_6_9_2_245_0/ %G en %F AFST_2000_6_9_2_245_0
Massart, Pascal. Some applications of concentration inequalities to statistics. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 9 (2000) no. 2, pp. 245-303. http://archive.numdam.org/item/AFST_2000_6_9_2_245_0/
[1] ). - Information theory and an extension of the maximum likelihood principle. In P.N. Petrov and F. Csaki, editors, Proceedings 2nd International Symposium on Information Theory, pages 267-281. Akademia Kiado, Budapest, 1973. | MR | Zbl
[2] ). - Model selection for regression on a fixed design. Technical report #97.49, (1997) Université Paris-Sud (to appear in Probability Theory and Related Fields). | MR | Zbl
[3] ), ) and ) (1999). - Model selection for (auto)regression with dependent data. Technical Report LMENS 99-12. Ecole Normale Supérieure, Paris.
[4] ). - Probability inequalities for the sum of independent random variables. Journal of the American Statistical Association 57 33-45 (1962). | Zbl
[5] ). - Examples of inconsistency of maximum likelihood estimates. Sankhya Ser.A 20, 207-210 (1958). | MR | Zbl
[6] ) and ). - Approximation of density functions by sequences of exponential families. Ann. Statist., 19:1054-1347, 1991. | MR | Zbl
[7] ), ), ). - Risk bounds for model selection via penalization. Probab. Th. Rel. Fields. 113, 301-415 (1999). | MR | Zbl
[8] ) and ). - Rates of convergence for minimum contrast estimators. Probab. Th. Relat. Fields 97, 113-150 (1993). | MR | Zbl
[9] ) and ). - Minimum contrast estimators on sieves: exponential bounds and rates of convergence. Bernoulli, 4(3), 329-375 (1998). | MR | Zbl
[10] ) and ). - From model selection to adaptive estimation. In Festschrift for Lucien Lecam: Research Papers in Probability and Statistics (D. Pollard, E. Torgersen and G. Yang, eds.), 55-87 (1997) Springer-Verlag, New-York. | MR | Zbl
[11] ) and ). - Gaussian model selection. Technical report (1999).
[12] ) and ). - A generalized cross-validation criterion for density estimation. Unpublished manuscript.
[13] ) and ). - How many bins should be put in a regular histogram. Unpublished manuscript.
[14] ). - On Gross' and Talagrand's inequalities on the discrete cube. Vestnik of Syktyvkar University Ser. 1,1 12-19 (1995) (in Russian). | MR | Zbl
[15] ). - The Brunn-Minkowski inequality in Gauss space. Invent. Math. 30, 207-216 (1975). | MR | Zbl
[16] ), ) and ). - A sharp concentration inequality with applications. Technical report # 99.25 (1999), Université de Paris-Sud. | MR
[17] ), ) and ). - Norm of Gaussian sample function. In Proceedings of the 3rd Japan-U.S.S.R. Symposium on Probability Theory, Lecture Notes in Mathematics 550 20-41 (1976) Springer-Verlag, Berlin. | MR | Zbl
[18] ) and ). - Extremal properties of half spaces for spherically invariant measures. J. Soviet. Math. 9, 9-18 (1978); translated from Zap. Nauch. Sem. L.O.M.I. 41, 14-24 (1974). | MR | Zbl
[19] ) and ). - Elements of Information Theory. Wiley series in telecommunications. Wiley (1991). | MR | Zbl
[20] ). - Information inequalities and concentration of measure. Ann. Prob. 25 927-939 (1997). | MR | Zbl
[21] ) and ). - Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425-455 (1994) | MR | Zbl
[22] ) Logarithmic Sobolev inequalities. Amer. J. Math. 97 1061-1083 (1975). | MR | Zbl
[23] ). - Modified Akaike's criterion for histogram density estimation. Technical report #99.61, (1999) Université de Paris-Sud.
[24] ). - Density estimation via exponential model selection. Technical report (1999).
[25] ). - Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58 13-30 (1963). | MR | Zbl
[26] ) and ). - Minimax theory of of image reconstruction. Lectures notes in Statistics 82, Soringer Verlag, NewYork (1993). | MR | Zbl
[27] ). - Isoperimetry and Gaussian Analysis. In Probabilités de St-Flour XXIV-1994 (P. Bernard, ed.), 165-294 (1996) Springer, Berlin. | MR | Zbl
[28] ). - On Talagrand deviation inequalities for product measures. ESAIM: Probability and Statistics 1, 63-87 (1996) http://www.emath.fr/ps/. | Numdam | MR | Zbl
[29] ) and ). - Probability in Banach spaces (Isoperimetry and processes). Ergebnisse der Mathematik und ihrer Grenzgebiete (1991) Springer-Verlag. | MR | Zbl
[30] ). - A simple proof of the blowing up lemma. IEEE Trans. Inform. Theory IT-32 445-446 (1986). | MR | Zbl
[31] ). - Bounding d-distance by information divergence: a method to prove measure concentration. Ann. Prob. 24 927-939 (1996). | MR | Zbl
[32] ) and ) A refinement of the KMT inequality for the uniform empirical process. Ann. Prob. 15, 871-884 (1987). | MR | Zbl
[33] ). - About the constants in Talagrand's concentration inequalities for empirical processes. Ann. Prob. (To appear)(2000). | MR | Zbl
[34] ). - Optimal constants for Hoeffding type inequalities. Technical report (1998).
[35] ). - On the method of bounded differences. In Surveys in Combinatorics 1989, pages 148-188. Cambridge University Press, Cambridge, 1989. | MR | Zbl
[36] ). - An isoperimetric theorem on the cube and the Khintchine-Kahane inequalities in product spaces. Proc. Amer. Math. Soc. 104 905-909 (1988). | MR | Zbl
[37] ). - Concentration of measure and isoperimetric inequalities in product spaces. Publications Mathématiques de l'I.H.E.S. 81 73-205 (1995). | Numdam | MR | Zbl
[38] ). - Sharper bounds for empirical processes. Annals of Probability 22, 28-76 (1994). | MR | Zbl
[39] ). - New concentration inequalities in product spaces. Invent. Math. 126, 505-563 (1996). | MR | Zbl
[40] ). - Estimation of dependencies based on empirical data. Springer, New York. | Zbl
[41] ). - Statistical learning theory. J. Wiley, New York. | MR | Zbl
[42] ). - Asymptotic statistics. Cambridge University Press (1998). | MR | Zbl
[43] ) and ) Weak Convergence and Empirical Processes. Springer, New York (1996). | MR | Zbl
