Estimates of the rate of approximation in a de-poissonization lemma

Andrei Yu. Zaitsev

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

  • Volume: 38, Issue: 6, page 1071-1086
  • ISSN: 0246-0203

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Zaitsev, Andrei Yu.. "Estimates of the rate of approximation in a de-poissonization lemma." Annales de l'I.H.P. Probabilités et statistiques 38.6 (2002): 1071-1086. <http://eudml.org/doc/77739>.

@article{Zaitsev2002,
author = {Zaitsev, Andrei Yu.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {strong approximation; Prokhorov distance; central limit theorem},
language = {eng},
number = {6},
pages = {1071-1086},
publisher = {Elsevier},
title = {Estimates of the rate of approximation in a de-poissonization lemma},
url = {http://eudml.org/doc/77739},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Zaitsev, Andrei Yu.
TI - Estimates of the rate of approximation in a de-poissonization lemma
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 6
SP - 1071
EP - 1086
LA - eng
KW - strong approximation; Prokhorov distance; central limit theorem
UR - http://eudml.org/doc/77739
ER -

References

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  1. [1] J. Beirlant, D.M. Mason, On the asymptotic normality of Lp-norms of empirical functionals, Math. Methods Statist.4 (1995) 1-19. Zbl0831.62019MR1324687
  2. [2] I. Berkes, W. Philipp, Approximation theorems for independent and weakly dependent random vectors, Ann. Probab.7 (1979) 29-54. Zbl0392.60024MR515811
  3. [3] R.M. Dudley, Probability and Metrics, Lectures Notes Aarhus Univ., 1976. 
  4. [4] W. Feller, An Introduction to Probability Theory and its Applications, Vol. II, Wiley, New York, 1966. Zbl0138.10207MR210154
  5. [5] E. Giné, D.M. Mason, A.Yu. Zaitsev, The L1-norm density estimator process, Ann. Probab., 2001, Accepted for publication. Zbl1031.62026MR1964947
  6. [6] A.Yu. Zaitsev, Estimates of the Lévy–Prokhorov distance in the multivariate central limit theorem for random variables with finite exponential moments, Theor. Probab. Appl.31 (1986) 203-220. Zbl0659.60042
  7. [7] A.Yu. Zaitsev, Estimates for quantiles of smooth conditional distributions and multidimensional invariance principle, Siberian Math. J.37 (1996) 807-831, (in Russian). Zbl0881.60034MR1643370
  8. [8] A.Yu. Zaitsev, Multidimensional version of the results of Komlós, Major and Tusnády for vectors with finite exponential moments, ESAIM: Probability and Statistics2 (1998) 41-108. Zbl0897.60033MR1616527
  9. [9] A.Yu. Zaitsev, Multidimensional version of the results of Sakhanenko in the invariance principle for vectors with finite exponential moments. I; II; III, Theor. Probab. Appl.45 (2000) 718-738, 46 (2001) 535–561; 744–769. Zbl0994.60029

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