The almost sure invariance principle for the empirical process of U-statistic structure
Dehling, Herold ; Denker, Manfred ; Philipp, Walter
Annales de l'I.H.P. Probabilités et statistiques, Tome 23 (1987), p. 121-134 / Harvested from Numdam
Publié le : 1987-01-01
@article{AIHPB_1987__23_2_121_0,
     author = {Dehling, Herold and Denker, Manfred and Philipp, Walter},
     title = {The almost sure invariance principle for the empirical process of U-statistic structure},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {23},
     year = {1987},
     pages = {121-134},
     mrnumber = {891707},
     zbl = {0619.60036},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1987__23_2_121_0}
}
Dehling, Herold; Denker, Manfred; Philipp, Walter. The almost sure invariance principle for the empirical process of U-statistic structure. Annales de l'I.H.P. Probabilités et statistiques, Tome 23 (1987) pp. 121-134. http://gdmltest.u-ga.fr/item/AIHPB_1987__23_2_121_0/

[1] G. Bennett, Probability inequalities for the sum of independent random variables. JASA, t. 57, 1962, p. 33-45. | Zbl 0104.11905

[2] S. Csörgö, L. Horvath, R. Serfling, An approximation for the empirical process of U-statistic structure. Technical report, Johns Hopkins University, 1983.

[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. | MR 690575 | Zbl 0488.60044

[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] 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. | MR 760694 | Zbl 0554.62014

[6] R. Serfling, Approximation Theorems of Mathematical Statistics. John Wiley and Sons, New York, 1980. | MR 595165 | Zbl 0538.62002

[7] R. Serfling, Generalized L-, M- and R-statistics. Ann. Stat., t. 12, 1984, p. 76-86. | MR 733500 | Zbl 0538.62015

[8] B.W. Silverman, Limit theorems for dissociated random variables. Adv. Appl. Prob., t. 8, 1976, p. 806-819. | MR 431348 | Zbl 0355.60026

[9] B.W. Silverman, Convergence of a class of empirical distribution functions of dependent random variables. Ann. Prob., t. 11, 1983, p. 745-751. | MR 704560 | Zbl 0514.60040