Moderate deviations for functional U-processes

Peter Eichelsbacher

Annales de l'I.H.P. Probabilités et statistiques (2001)

  • Volume: 37, Issue: 2, page 245-273
  • ISSN: 0246-0203

How to cite

top

Eichelsbacher, Peter. "Moderate deviations for functional U-processes." Annales de l'I.H.P. Probabilités et statistiques 37.2 (2001): 245-273. <http://eudml.org/doc/77689>.

@article{Eichelsbacher2001,
author = {Eichelsbacher, Peter},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {moderate deviations; -processes; partial sums; VC-classes; decoupling inequality; maximal inequality for -statistics; Bernstein-type inequality},
language = {eng},
number = {2},
pages = {245-273},
publisher = {Elsevier},
title = {Moderate deviations for functional U-processes},
url = {http://eudml.org/doc/77689},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Eichelsbacher, Peter
TI - Moderate deviations for functional U-processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2001
PB - Elsevier
VL - 37
IS - 2
SP - 245
EP - 273
LA - eng
KW - moderate deviations; -processes; partial sums; VC-classes; decoupling inequality; maximal inequality for -statistics; Bernstein-type inequality
UR - http://eudml.org/doc/77689
ER -

References

top
  1. [1] M.A Arcones, E Giné, Limit theorems for U-processes, Ann. Probab.21 (1993) 1494-1542. Zbl0789.60031MR1235426
  2. [2] M.A Arcones, E Giné, U-processes indexed by Vapnik–Červonenkis classes of functions with applications to asymptotics and bootstrap of U-statistics with estimated parameters, Stochastic Process. Appl.52 (1994) 17-38. Zbl0807.62014MR1289166
  3. [3] M.A Arcones, E Giné, On the law of the iterated logarithm for canonical U-statistics and processes, Stochastic Process. Appl.58 (1995) 217-245. Zbl0829.60003MR1348376
  4. [4] P Baldi, Large deviations and stochastic homogenization, Ann. Mat. Pura Appl.151 (1988) 161-177. Zbl0654.60024MR964508
  5. [5] A.A Borovkov, A.A Mogulskii, Probabilities of large deviations in topological spaces I, Siberian Math. J.19 (1978) 697-709. Zbl0413.60021MR508496
  6. [6] A.A Borovkov, A.A Mogulskii, Probabilities of large deviations in topological spaces II, Siberian Math. J.21 (1980) 653-664. Zbl0458.60019MR592213
  7. [7] Yu.V Borovskikh, U-Statistics in Banach Spaces, VSP, Utrecht, 1996. Zbl0865.60004MR1419498
  8. [8] A Dembo, T Zajic, Uniform large and moderate deviations for functional empirical processes, Stochastic Process. Appl.67 (1997) 195-211. Zbl0890.60022MR1449831
  9. [9] A Dembo, O Zeitouni, Large Deviations Techniques and Applications, Springer, New York, 1998. Zbl0896.60013MR1619036
  10. [10] R.M Dudley, A course on empirical processes, in: Dold A, Eckmann B (Eds.), École d'Eté de Probabilités de Saint-Flour XII, Lecture Notes in Math., 1097, Springer, New York, 1984, pp. 1-142. Zbl0554.60029MR876079
  11. [11] P Eichelsbacher, Large deviations for products of empirical probability measures in the τ-topology, J. Theoret. Probab.10 (4) (1997) 903-920. Zbl0891.60031
  12. [12] P Eichelsbacher, M Löwe, Large deviations for partial sums U-processes, Theory Probab. Appl.43 (1998) 97-115. Zbl0927.60047MR1669988
  13. [13] P Eichelsbacher, U Schmock, Exponential approximations in completely regular topological spaces and extensions of Sanov's theorem, Stochastic Process. Appl.77 (2) (1998) 233-251. Zbl0934.60023MR1649006
  14. [14] P Eichelsbacher, U Schmock, Large and rank-dependent moderate deviations for U-empirical measures in strong topologies, preprint, 1998. Zbl1039.60023MR1981633
  15. [15] E Giné, V de la Peña, Decoupling: From Dependence to Independence, Springer-Verlag, 1999. Zbl0918.60021MR1666908
  16. [16] E Giné, C.-H Zhang, On integrability in the LIL for degenerate U-statistics, J. Theoret. Probab.9 (2) (1996) 385-412. Zbl0873.60015MR1385404
  17. [17] P Hall, On the invariance principle for U-statistics, Stochastic Process. Appl.9 (1979) 163-174. Zbl0422.62019MR548836
  18. [18] W Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc.58 (1963) 13-30. Zbl0127.10602MR144363
  19. [19] M Ledoux, M Talagrand, Probability in Banach Spaces, Springer-Verlag, Berlin, 1991. Zbl0748.60004MR1102015
  20. [20] A Mandelbaum, M.S Taqqu, Invariance principle for symmetric statistics, Ann. Statist.12 (1984) 483-496. Zbl0547.60039MR740907
  21. [21] R.G Miller, P.K Sen, Weak convergence of U-statistics and von Mises differentiable, Ann. Math. Statist.43 (1972) 31-41. Zbl0238.62057MR300321
  22. [22] A.A Mogulskii, Large deviations for trajectories of multidimensional random walks, Theory Probab. Appl.21 (1976) 300-315. Zbl0366.60031MR420798
  23. [23] S.J Montgomery-Smith, Comparison of sums of independent identically distributed random vectors, Probab. Math. Statist.14 (2) (1994) 281-285. Zbl0827.60005MR1321767
  24. [24] S.J Montgomery-Smith, V de la Peña, Decoupling inequalities for the tail probabilities of multivariate U-statistics, Ann. Probab.23 (2) (1995) 806-816. Zbl0827.60014MR1334173
  25. [25] D Pollard, Convergence of Stochastic Processes, Springer, New York, 1984. Zbl0544.60045MR762984
  26. [26] M Talagrand, Sharper bounds for gaussian and empirical processes, Ann. Probab.22 (1) (1994) 28-76. Zbl0798.60051MR1258865
  27. [27] L Wu, Large deviations, moderate deviations and LIL for empirical processes, Ann. Probab.22 (1) (1994) 17-27. Zbl0793.60032MR1258864
  28. [28] V.V Yurinsky, Exponential inequalities for sums of random vectors, J. Mult. Anal.6 (4) (1976) 473-499. Zbl0346.60001MR428401
  29. [29] V.V Yurinsky, Sums and Gaussian Vectors, Lecture Notes in Mathematics, 1617, Springer-Verlag, Berlin, 1995. Zbl0846.60003MR1442713

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.