Maximal inequalities via bracketing with adaptive truncation

David Pollard

Annales de l'I.H.P. Probabilités et statistiques (2002)

  • Volume: 38, Issue: 6, page 1039-1052
  • ISSN: 0246-0203

How to cite

top

Pollard, David. "Maximal inequalities via bracketing with adaptive truncation." Annales de l'I.H.P. Probabilités et statistiques 38.6 (2002): 1039-1052. <http://eudml.org/doc/77736>.

@article{Pollard2002,
author = {Pollard, David},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {bracketing; adaptive truncation; empirical process; functional central limit theorem},
language = {eng},
number = {6},
pages = {1039-1052},
publisher = {Elsevier},
title = {Maximal inequalities via bracketing with adaptive truncation},
url = {http://eudml.org/doc/77736},
volume = {38},
year = {2002},
}

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
PB - Elsevier
VL - 38
IS - 6
SP - 1039
EP - 1052
LA - eng
KW - bracketing; adaptive truncation; empirical process; functional central limit theorem
UR - http://eudml.org/doc/77736
ER -

References

top
  1. [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. Zbl0595.60027MR832025
  2. [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. Zbl0618.60022MR927241
  3. [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. Zbl0575.60034MR807339
  4. [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. Zbl0572.60037MR723727
  5. [5] L. Birgé, P. Massart, Rates of convergence for minimum contrast estimators, Probab. Theory Related Fields97 (1993) 113-150. Zbl0805.62037MR1240719
  6. [6] M.D. Donsker, Justification and extension of Doob's heuristic approach to the Kolmogorov–Smirnov theorems, Ann. Math. Statist.23 (1952) 277-281. Zbl0046.35103
  7. [7] P. Doukhan, P. Massart, E. Rio, Invariance principle for absolutely regular processes, Ann. Institut H. Poincaré31 (1995) 393-427. Zbl0817.60028MR1324814
  8. [8] R.M. Dudley, Central limit theorems for empirical measures, Ann. Probab.6 (1978) 899-929. Zbl0404.60016MR512411
  9. [9] R.M. Dudley, Donsker classes of functions, in: Csörgo&#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. Zbl0468.60009MR665285
  10. [10] M. Ledoux, M. Talagrand, Probability in Banach Spaces: Isoperimetry and Processes, Springer, New York, 1991. Zbl0748.60004MR1102015
  11. [11] P. Massart, Rates of convergence in the central limit theorem for empirical processes, Ann. Institut H. Poincaré22 (1986) 381-423. Zbl0615.60032MR871904
  12. [12] M. Ossiander, A central limit theorem under metric entropy with L2 bracketing, Ann. Probab.15 (1987) 897-919. Zbl0665.60036MR893905
  13. [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. Zbl0517.60043MR717231
  14. [14] D. Pollard, A User's Guide to Measure Theoretic Probability, Cambridge University Press, Cambridge, 2001. Zbl0992.60001
  15. [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. Zbl0497.60030MR696030
  16. [16] E. Rio, Covariance inequalities for strongly mixing processes, Ann. Institut H. Poincaré29 (1993) 587-597. Zbl0798.60027MR1251142

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.