Tusnady's lemma, 24 years later

Pascal Massart

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

  • Volume: 38, Issue: 6, page 991-1007
  • ISSN: 0246-0203

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Massart, Pascal. "Tusnady's lemma, 24 years later." Annales de l'I.H.P. Probabilités et statistiques 38.6 (2002): 991-1007. <http://eudml.org/doc/77752>.

@article{Massart2002,
author = {Massart, Pascal},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {quantile transform; coupling; binomial random variable; normal random variable},
language = {eng},
number = {6},
pages = {991-1007},
publisher = {Elsevier},
title = {Tusnady's lemma, 24 years later},
url = {http://eudml.org/doc/77752},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Massart, Pascal
TI - Tusnady's lemma, 24 years later
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 6
SP - 991
EP - 1007
LA - eng
KW - quantile transform; coupling; binomial random variable; normal random variable
UR - http://eudml.org/doc/77752
ER -

References

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  1. [1] J. Bretagnolle, P. Massart, Hungarian constructions from the nonasymptotic view point, Ann. Probab.17 (1) (1989) 239-256. Zbl0667.60042MR972783
  2. [2] M. Csörgo&#x030B;, P. Révész, Strong Approximations in Probability and Statistics, Academic Press, New York, 1981. Zbl0539.60029MR666546
  3. [3] A. Carter, D. Pollard, Tusnády's inequality revisited, Preprint, 2000. 
  4. [4] K. Ito, H.P. Mac Kean, Diffusion Processes and Their Sample Paths, Springer, Berlin, 1965. 
  5. [5] J. Komlós, P. Major, G. Tusnády, An approximation of partial sums of independent rv-s, and the sample df. I, Z. Warscheinlichkeitstheorie Verwandte Geb.32 (1975) 111-131. Zbl0308.60029MR375412
  6. [6] D. Mason, W. van Zwet, A refinement of the KMT inequality for the uniform empirical process, Ann. Probab.15 (1987) 871-884. Zbl0638.60040MR893903
  7. [7] M. Nussbaum, Asymptotic equivalence of density estimation and Gaussian white noise, Ann. Statist.24 (1996) 2399-2430. Zbl0867.62035MR1425959
  8. [8] G.R. Shorack, J.A. Wellner, Empirical Processes with Applications to Statistics, Wiley, New York, 1986. Zbl1170.62365MR838963
  9. [9] G. Tusnády, A study of statistical hypotheses, PhD Thesis, Hungarian Academy of Sciences, Budapest, 1977 (In Hungarian). 

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