Maximal inequalities via bracketing with adaptive truncation
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 6, pp. 1039-1052. 
@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},
     pages = {1039--1052},
     publisher = {Elsevier},
     volume = {38},
     number = {6},
     year = {2002},
     mrnumber = {1955351},
     zbl = {1019.60015},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2002__38_6_1039_0/}
}
TY  - JOUR
AU  - Pollard, David
TI  - Maximal inequalities via bracketing with adaptive truncation
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2002
SP  - 1039
EP  - 1052
VL  - 38
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/item/AIHPB_2002__38_6_1039_0/
LA  - en
ID  - AIHPB_2002__38_6_1039_0
ER  - 
%0 Journal Article
%A Pollard, David
%T Maximal inequalities via bracketing with adaptive truncation
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2002
%P 1039-1052
%V 38
%N 6
%I Elsevier
%U http://www.numdam.org/item/AIHPB_2002__38_6_1039_0/
%G en
%F 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) no. 6, pp. 1039-1052. http://www.numdam.org/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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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

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

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

[9] R.M. Dudley, Donsker classes of functions, in: Csörgo&Amp;#X030B; 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 | Zbl

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

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

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

[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 | Zbl

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

[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 | Zbl

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