Strong approximations of bivariate uniform empirical processes

Nathalie Castelle; Françoise Laurent-Bonvalot

Annales de l'I.H.P. Probabilités et statistiques (1998)

  • Volume: 34, Issue: 4, page 425-480
  • ISSN: 0246-0203

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Castelle, Nathalie, and Laurent-Bonvalot, Françoise. "Strong approximations of bivariate uniform empirical processes." Annales de l'I.H.P. Probabilités et statistiques 34.4 (1998): 425-480. <http://eudml.org/doc/77609>.

@article{Castelle1998,
author = {Castelle, Nathalie, Laurent-Bonvalot, Françoise},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {strong approximation; bivariate empirical process; Brownian bridges; Gaussian Kiefer process; hypergeometric distribution},
language = {eng},
number = {4},
pages = {425-480},
publisher = {Gauthier-Villars},
title = {Strong approximations of bivariate uniform empirical processes},
url = {http://eudml.org/doc/77609},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Castelle, Nathalie
AU - Laurent-Bonvalot, Françoise
TI - Strong approximations of bivariate uniform empirical processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1998
PB - Gauthier-Villars
VL - 34
IS - 4
SP - 425
EP - 480
LA - eng
KW - strong approximation; bivariate empirical process; Brownian bridges; Gaussian Kiefer process; hypergeometric distribution
UR - http://eudml.org/doc/77609
ER -

References

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  1. [1] Adler R.J. and Brown L.D., Tail of behaviour for suprema of empirical process. Annals of probability, Vol 14, 1986, pp. 1-30. Zbl0596.62053MR815959
  2. [2] Bennett G., Probability inequalities for the sum of independants random variables.J. AM. Statis. Assoc., Vol. 57, 1962, pp. 33-45. Zbl0104.11905
  3. [3] Bretagnolle J. and Massart P., Hungarian constructions from the non asymptotic view point. Annals of Probability, Vol 17, 1989, pp. 239-256. Zbl0667.60042MR972783
  4. [4] Brillinger D.R., The asymptotic representation of the sample distribution function. Bull. Amer. Math. Soc., Vol 75, 1969, pp. 545-547. Zbl0206.20602MR243659
  5. [5] Csörgö M. and Revesz P., Strong approximations in probability and statistics. Academic Press, 1981, New York. Zbl0539.60029MR666546
  6. [6] Csáki E., Investigations concerning the empirical distribution function. English translation in SelectedTrans. Math. Statis. Probab., Vol 15, 1981, pp. 229-317. Zbl0478.62038
  7. [7] Csörgö M. and Horváth L., Weighted Approximations in Probability and Statistics. Wiley & Sons, 1993. Zbl0770.60038
  8. [8] Doob J.L., Stochastic process, Wiley, 1953, New York. Zbl0053.26802MR58896
  9. [9] Dvoretzky A., Kiefer J.C. and Wolfowitz J., Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. Ann. Math. Stat., Vol. 33, 1956, pp. 642-669. Zbl0073.14603MR83864
  10. [10] Kieffer J., On the deviations in the Skorohod-Strassen approximation scheme.Z. Wahrschein. Verw. Geb., Vol. 13, 1969, pp. 321-332. Zbl0176.48201MR256461
  11. [11] Kiefer J., Skorohod embedding of multivariate R. V.'s, and the sample D.F.Z. Z. Wahrschein. Verw. Geb., Vol. 24, 1972, pp. 1-35. Zbl0267.60034MR341636
  12. [12] Komlós J., Major P. and Tusnády, G., An approximation of partial sums of independent RV'- and the sampleD. F. I. Z. Warschein. Verw. Geb., Vol. 32, 1975, pp. 111-131. Zbl0308.60029MR375412
  13. [13] Mason D., A strong invariance theorem for the tail empirical process. Annales de l'I.H.P., Vol. 24, 1988. Zbl0664.60038MR978022
  14. [14] Mason D. and Van Zwet R., A refinement of the KMT inequality for the uniform empirical process. Annals of Probability, Vol. 15, 1987, pp. 871-884. Zbl0638.60040MR893903
  15. [15] Massart P., The tight constant of the Dvorestsky-Kiefer-Wolfowitz inequality. Annals of Probability, Vol. 18, 1990, pp.1269-1283. Zbl0713.62021MR1062069
  16. [16] Shorack G.R. and Wellner J.A., Empirical processes with applications to statistics. Wiley & Sons, 1986. Zbl1170.62365
  17. [17] Skorohod A.V., On a representation of random variables. Th. Proba. Appl., Vol. 21, 1976, pp. 628-632. Zbl0362.60004MR428369
  18. [18] Talagrand M., Sharper bounds for empirical process. Annals of Probability, Vol. 22, 1994, pp. 28-76. Zbl0798.60051MR1258865
  19. [19] Tusnady G., A remark on the approximation of the sample D.F. in the multidimensional case. PeriodicaMath. Hung., Vol. 8, 1977, pp. 53-55. Zbl0386.60006MR443045
  20. [20] Wellner J., Limit theorems for the ratio of the empirical distribution function to the true distribution function. Z. Warschein. Verw. Geb., Vol. 45, 1978, pp. 73-88. Zbl0382.60031MR651392

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