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 , p. 245-303
Zbl 0986.62002 | MR 1813803 | 8 citations dans Numdam
URL stable : http://www.numdam.org/item?id=AFST_2000_6_9_2_245_0

Bibliographie

[1] Akaike (H.). - 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 483125 | Zbl 0283.62006

[2] Baraud (Y.). - 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 1777129 | Zbl 0997.62027

[3] Baraud (Y.), Comte (F.) and Viennet (G.) (1999). - Model selection for (auto)regression with dependent data. Technical Report LMENS 99-12. Ecole Normale Supérieure, Paris.

[4] Bennett (G.). - Probability inequalities for the sum of independent random variables. Journal of the American Statistical Association 57 33-45 (1962). Zbl 0104.11905

[5] Bahadur (R.R.). - Examples of inconsistency of maximum likelihood estimates. Sankhya Ser.A 20, 207-210 (1958). MR 107331 | Zbl 0087.34202

[6] Barron (A.R.) and Sheu (C.H.). - Approximation of density functions by sequences of exponential families. Ann. Statist., 19:1054-1347, 1991. MR 1126328 | Zbl 0739.62027

[7] Barron (A.R.), Birgé (L.), Massart (P.). - Risk bounds for model selection via penalization. Probab. Th. Rel. Fields. 113, 301-415 (1999). MR 1679028 | Zbl 0946.62036

[8] Birgé (L.) and Massart (P.). - Rates of convergence for minimum contrast estimators. Probab. Th. Relat. Fields 97, 113-150 (1993). MR 1240719 | Zbl 0805.62037

[9] Birgé (L.) and Massart (P.). - Minimum contrast estimators on sieves: exponential bounds and rates of convergence. Bernoulli, 4(3), 329-375 (1998). MR 1653272 | Zbl 0954.62033

[10] Birgé (L.) and Massart (P.). - 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 1462939 | Zbl 0920.62042

[11] Birgé (L.) and Massart (P.). - Gaussian model selection. Technical report (1999).

[12] Birgé (L.) and Massart (P.). - A generalized cross-validation criterion for density estimation. Unpublished manuscript.

[13] Birgé (L.) and Rozenholc (Y.). - How many bins should be put in a regular histogram. Unpublished manuscript.

[14] Bobkov (S.). - On Gross' and Talagrand's inequalities on the discrete cube. Vestnik of Syktyvkar University Ser. 1,1 12-19 (1995) (in Russian). MR 1717705 | Zbl 1011.60500

[15] Borell (C.). - The Brunn-Minkowski inequality in Gauss space. Invent. Math. 30, 207-216 (1975). MR 399402 | Zbl 0311.60007

[16] Boucheron (S.), Lugosi (G.) and Massart (P.). - A sharp concentration inequality with applications. Technical report # 99.25 (1999), Université de Paris-Sud. MR 1749290

[17] Cirel'Son (B.S.), Ibragimov (I.A.) and Sudakov (V.N.). - 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 458556 | Zbl 0359.60019

[18] Cirel'Son (B.S.) and Sudakov (V.N.). - 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 365680 | Zbl 0395.28007

[19] Cover (T.M.) and Thomas (J.A.). - Elements of Information Theory. Wiley series in telecommunications. Wiley (1991). MR 1122806 | Zbl 0762.94001

[20] Dembo (A.). - Information inequalities and concentration of measure. Ann. Prob. 25 927-939 (1997). MR 1434131 | Zbl 0880.60018

[21] Donoho (D.L.) and Johnstone (I.M.). - Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425-455 (1994) MR 1311089 | Zbl 0815.62019

[22] Gross (L.) Logarithmic Sobolev inequalities. Amer. J. Math. 97 1061-1083 (1975). MR 420249 | Zbl 0318.46049

[23] Castellan (G.). - Modified Akaike's criterion for histogram density estimation. Technical report #99.61, (1999) Université de Paris-Sud.

[24] Castellan (G.). - Density estimation via exponential model selection. Technical report (1999).

[25] Hoeffding (W.). - Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58 13-30 (1963). MR 144363 | Zbl 0127.10602

[26] Korostelev (A.P.) and Tsybakov (A.B.). - Minimax theory of of image reconstruction. Lectures notes in Statistics 82, Soringer Verlag, NewYork (1993). MR 1226450 | Zbl 0833.62039

[27] Ledoux (M.). - Isoperimetry and Gaussian Analysis. In Probabilités de St-Flour XXIV-1994 (P. Bernard, ed.), 165-294 (1996) Springer, Berlin. MR 1600888 | Zbl 0874.60005

[28] Ledoux (M.). - On Talagrand deviation inequalities for product measures. ESAIM: Probability and Statistics 1, 63-87 (1996) http://www.emath.fr/ps/. Numdam | MR 1399224 | Zbl 0869.60013

[29] Ledoux (M.) and Talagrand (M.). - Probability in Banach spaces (Isoperimetry and processes). Ergebnisse der Mathematik und ihrer Grenzgebiete (1991) Springer-Verlag. MR 1102015 | Zbl 0748.60004

[30] Marton (K.). - A simple proof of the blowing up lemma. IEEE Trans. Inform. Theory IT-32 445-446 (1986). MR 838213 | Zbl 0594.94003

[31] Marton (K.). - Bounding d-distance by information divergence: a method to prove measure concentration. Ann. Prob. 24 927-939 (1996). MR 1404531 | Zbl 0865.60017

[32] Mason (D.M.) and Van Zwet (W.R.) A refinement of the KMT inequality for the uniform empirical process. Ann. Prob. 15, 871-884 (1987). MR 893903 | Zbl 0638.60040

[33] Massart (P.). - About the constants in Talagrand's concentration inequalities for empirical processes. Ann. Prob. (To appear)(2000). MR 1782276 | Zbl 01905939

[34] Massart (P.). - Optimal constants for Hoeffding type inequalities. Technical report (1998).

[35] Mcdiarmid (C.). - On the method of bounded differences. In Surveys in Combinatorics 1989, pages 148-188. Cambridge University Press, Cambridge, 1989. MR 1036755 | Zbl 0712.05012

[36] Talagrand (M.). - An isoperimetric theorem on the cube and the Khintchine-Kahane inequalities in product spaces. Proc. Amer. Math. Soc. 104 905-909 (1988). MR 964871 | Zbl 0691.60015

[37] Talagrand (M.). - Concentration of measure and isoperimetric inequalities in product spaces. Publications Mathématiques de l'I.H.E.S. 81 73-205 (1995). Numdam | MR 1361756 | Zbl 0864.60013

[38] Talagrand (M.). - Sharper bounds for empirical processes. Annals of Probability 22, 28-76 (1994). MR 1258865 | Zbl 0798.60051

[39] Talagrand (M.). - New concentration inequalities in product spaces. Invent. Math. 126, 505-563 (1996). MR 1419006 | Zbl 0893.60001

[40] Vapnik (V.N.). - Estimation of dependencies based on empirical data. Springer, New York. Zbl 0499.62005

[41] Vapnik (V.N.). - Statistical learning theory. J. Wiley, New York. MR 1641250 | Zbl 0935.62007

[42] Van Der Vaart (A.). - Asymptotic statistics. Cambridge University Press (1998). MR 1652247 | Zbl 0910.62001

[43] Van Der Vaart (A.) and Wellner (J.) Weak Convergence and Empirical Processes. Springer, New York (1996). MR 1385671 | Zbl 0862.60002