Weak convergence for empirical processes of associated sequences
Annales de l'I.H.P. Probabilités et statistiques, Volume 36 (2000) no. 5, pp. 547-567.
@article{AIHPB_2000__36_5_547_0,
     author = {Louhichi, Sana},
     title = {Weak convergence for empirical processes of associated sequences},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {547--567},
     publisher = {Gauthier-Villars},
     volume = {36},
     number = {5},
     year = {2000},
     zbl = {0968.60019},
     mrnumber = {1792655},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2000__36_5_547_0/}
}
TY  - JOUR
AU  - Louhichi, Sana
TI  - Weak convergence for empirical processes of associated sequences
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2000
DA  - 2000///
SP  - 547
EP  - 567
VL  - 36
IS  - 5
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_2000__36_5_547_0/
UR  - https://zbmath.org/?q=an%3A0968.60019
UR  - https://www.ams.org/mathscinet-getitem?mr=1792655
LA  - en
ID  - AIHPB_2000__36_5_547_0
ER  - 
%0 Journal Article
%A Louhichi, Sana
%T Weak convergence for empirical processes of associated sequences
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2000
%P 547-567
%V 36
%N 5
%I Gauthier-Villars
%G en
%F AIHPB_2000__36_5_547_0
Louhichi, Sana. Weak convergence for empirical processes of associated sequences. Annales de l'I.H.P. Probabilités et statistiques, Volume 36 (2000) no. 5, pp. 547-567. http://www.numdam.org/item/AIHPB_2000__36_5_547_0/

[1] Andrews D.W.K., Pollard D., An introduction to functional central limit theorems for dependent stochastic processes, Int. Stat. Rev. 62 (1994) 119-132. | Zbl

[2] Billingsley P., Probability and Measure, Wiley, New York, 1968.

[3] Bradley R.C., Basic properties of strong mixing conditions, in: Eberlein E., Taqqu M.S. (Eds.), Dependence in Probability and Statistics, Birkhäuser, Boston, 1986, pp. 165-192. | MR | Zbl

[4] Burton R.M., Dabrowski A.R., Dehling H., An invariance principle for weakly associated random variables, Stoch. Proc. Appl. 23 (1986) 301-306. | MR | Zbl

[5] Doukhan P., Mixing: Properties and Examples, Lecture Notes in Statist., Vol. 85, Springer-Verlag, Berlin, 1994. | MR | Zbl

[6] Doukhan P., Massart P., Rio E., Invariance principle for the empirical measure of a weakly dependent process, Ann. I.H.P. 31 (2) (1995) 393-427. | Numdam | MR | Zbl

[7] Esary J., Proschan F., Walkup D., Association of random variables with applications, Ann. Math. Stat. 38 (1967) 1466-1476. | MR | Zbl

[8] Giraitis L., Surgailis D., A central limit theorem for the empirical process of a long memory linear sequence, Preprint, 1994.

[9] Newman C.M., Asymptotic independence and limit theorems for positively and negatively dependent random variables, in: Tong Y.L. (Ed.), Inequalities in Statistics and Probability, I.M.S. Lecture Notes-Monograph Series, Vol. 5, 1984, pp. 127-140. | MR

[10] Petrov V.V., Limit Theorems of Probability Theory: Sequences of Independent Random Variables, Clarendon Press, Oxford, 1995. | MR | Zbl

[11] Pitt L., Positively correlated normal variables are associated, Ann. Probab. 10 (1982) 496-499. | MR | Zbl

[12] Pham T.D., Tran L.T., Some mixing properties of time series models, Stoch. Proc. Appl. 19 (1985) 297-303. | MR | Zbl

[13] Shao Q.M., Yu H., Weak convergence for weighted empirical processes of dependent sequences, Ann. Probab. 24 (4) (1996) 2052-2078. | MR | Zbl

[14] Volkonski V.A., Rozanov Y.A., Some limit theorems for random functions, Theory Probab. Appl. 4 (1959) 178-197. | MR | Zbl

[15] Yu H., A Glivenko-Cantelli lemma and weak convergence for empirical processes of associated sequences, Probab. Theory Related Fields 95 (1993) 357-370. | MR | Zbl