The almost sure invariance principle for the empirical process of U-statistic structure

Herold Dehling; Manfred Denker; Walter Philipp

Annales de l'I.H.P. Probabilités et statistiques (1987)

  • Volume: 23, Issue: 2, page 121-134
  • ISSN: 0246-0203

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Dehling, Herold, Denker, Manfred, and Philipp, Walter. "The almost sure invariance principle for the empirical process of U-statistic structure." Annales de l'I.H.P. Probabilités et statistiques 23.2 (1987): 121-134. <http://eudml.org/doc/77294>.

@article{Dehling1987,
author = {Dehling, Herold, Denker, Manfred, Philipp, Walter},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {empirical process of U-statistic structure; strong approximation; functional law of iterated logarithm; law of iterated logarithm for generalized L-statistics},
language = {eng},
number = {2},
pages = {121-134},
publisher = {Gauthier-Villars},
title = {The almost sure invariance principle for the empirical process of U-statistic structure},
url = {http://eudml.org/doc/77294},
volume = {23},
year = {1987},
}

TY - JOUR
AU - Dehling, Herold
AU - Denker, Manfred
AU - Philipp, Walter
TI - The almost sure invariance principle for the empirical process of U-statistic structure
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1987
PB - Gauthier-Villars
VL - 23
IS - 2
SP - 121
EP - 134
LA - eng
KW - empirical process of U-statistic structure; strong approximation; functional law of iterated logarithm; law of iterated logarithm for generalized L-statistics
UR - http://eudml.org/doc/77294
ER -

References

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  1. [1] G. Bennett, Probability inequalities for the sum of independent random variables. JASA, t. 57, 1962, p. 33-45. Zbl0104.11905
  2. [2] S. Csörgö, L. Horvath, R. Serfling, An approximation for the empirical process of U-statistic structure. Technical report, Johns Hopkins University, 1983. 
  3. [3] R.M. Dudley, W. Philipp, Invariance principles for sums of Banach space valued random elements and empirical processes. Zeitschrift Wahrscheinlichkeitstheorie verw. Gebiete, t. 62, 1983, p. 509-552. Zbl0488.60044MR690575
  4. [4] R. Helmers, P. Janssen, R. Serfling, Asymptotic theory for the e. d. f. of U-statistics and applications to GL-statistics and the bootstrap. Preprint, 1984-1985. 
  5. [5] P. Janssen, R. Serfling, N. Veraverbeke, Asymptotic normality for a general class of statistical functions and applications to measures of spread. Ann. Stat., t. 12, 1984, p. 1369-1379. Zbl0554.62014MR760694
  6. [6] R. Serfling, Approximation Theorems of Mathematical Statistics. John Wiley and Sons, New York, 1980. Zbl0538.62002MR595165
  7. [7] R. Serfling, Generalized L-, M- and R-statistics. Ann. Stat., t. 12, 1984, p. 76-86. Zbl0538.62015MR733500
  8. [8] B.W. Silverman, Limit theorems for dissociated random variables. Adv. Appl. Prob., t. 8, 1976, p. 806-819. Zbl0355.60026MR431348
  9. [9] B.W. Silverman, Convergence of a class of empirical distribution functions of dependent random variables. Ann. Prob., t. 11, 1983, p. 745-751. Zbl0514.60040MR704560

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