Maximal inequalities via bracketing with adaptive truncation
Pollard, David
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002), p. 1039-1052 / Harvested from Numdam
Publié le : 2002-01-01
@article{AIHPB_2002__38_6_1039_0,
     author = {Pollard, David},
     title = {Maximal inequalities via bracketing with adaptive truncation},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {38},
     year = {2002},
     pages = {1039-1052},
     mrnumber = {1955351},
     zbl = {1019.60015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2002__38_6_1039_0}
}
Pollard, David. Maximal inequalities via bracketing with adaptive truncation. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) pp. 1039-1052. http://gdmltest.u-ga.fr/item/AIHPB_2002__38_6_1039_0/

[1] K.S. Alexander, R. Pyke, A uniform central limit theorem for set-indexed partial-sum processes with finite variance, Ann. Probab. 14 (1986) 582-597. | MR 832025 | Zbl 0595.60027

[2] N.T. Andersen, E. Giné, M. Ossiander, J. Zinn, The central limit theorem and the law of the iterated logarithm for empirical processes under local conditions, Z. Wahrscheinlichkeitstheorie Verw. Geb. 77 (1988) 271-306. | MR 927241 | Zbl 0618.60022

[3] R.F. Bass, Law of the iterated logarithm for set-indexed partial-sum processes with finite variance, Z. Wahrscheinlichkeitstheorie Verw. Geb. 70 (1985) 591-608. | MR 807339 | Zbl 0575.60034

[4] R.F. Bass, R. Pyke, Functional law of the iterated logarithm and uniform central limit theorem for partial-sum processes indexed by sets, Ann. Probab. 12 (1984) 13-34. | MR 723727 | Zbl 0572.60037

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

[6] M.D. Donsker, Justification and extension of Doob's heuristic approach to the Kolmogorov-Smirnov theorems, Ann. Math. Statist. 23 (1952) 277-281. | Zbl 0046.35103

[7] P. Doukhan, P. Massart, E. Rio, Invariance principle for absolutely regular processes, Ann. Institut H. Poincaré 31 (1995) 393-427. | Numdam | MR 1324814 | Zbl 0817.60028

[8] R.M. Dudley, Central limit theorems for empirical measures, Ann. Probab. 6 (1978) 899-929. | MR 512411 | Zbl 0404.60016

[9] R.M. Dudley, Donsker classes of functions, in: Csörgő M., Dawson D.A., Rao J.N.K., Saleh A.K.Md.E. (Eds.), Statistics and Related Topics, North-Holland, Amsterdam, 1981, pp. 341-352. | MR 665285 | Zbl 0468.60009

[10] M. Ledoux, M. Talagrand, Probability in Banach Spaces: Isoperimetry and Processes, Springer, New York, 1991. | MR 1102015 | Zbl 0748.60004

[11] P. Massart, Rates of convergence in the central limit theorem for empirical processes, Ann. Institut H. Poincaré 22 (1986) 381-423. | Numdam | MR 871904 | Zbl 0615.60032

[12] M. Ossiander, A central limit theorem under metric entropy with L2 bracketing, Ann. Probab. 15 (1987) 897-919. | MR 893905 | Zbl 0665.60036

[13] G. Pisier, Some applications of the metric entropy condition to harmonic analysis, in: Lecture Notes in Mathematics, 995, Springer, New York, 1983, pp. 123-154. | MR 717231 | Zbl 0517.60043

[14] D. Pollard, A User's Guide to Measure Theoretic Probability, Cambridge University Press, Cambridge, 2001. | Zbl 0992.60001

[15] R. Pyke, A uniform central limit theorem for partial-sum processes indexed by sets, in: Kingman J.F.C., Reuter G.E.H. (Eds.), Probability, Statistics and Analysis, Cambridge University Press, Cambridge, 1983, pp. 219-240. | MR 696030 | Zbl 0497.60030

[16] E. Rio, Covariance inequalities for strongly mixing processes, Ann. Institut H. Poincaré 29 (1993) 587-597. | Numdam | MR 1251142 | Zbl 0798.60027