Testing stationary processes for independence
Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 4, pp. 1219-1225.

Soit H0 la classe de tous les processus indépendants et équidistribués à valeurs réelles, et H1 la classe complémentaire dans l'ensemble des processus ergodiques. Nous donnons un test séquentiel fortement consistant pour les distinguer.

Let H0 denote the class of all real valued i.i.d. processes and H1 all other ergodic real valued stationary processes. In spite of the fact that these classes are not countably tight we give a strongly consistent sequential test for distinguishing between them.

DOI : 10.1214/11-AIHP426
Classification : 62M07
Mots clés : independent processes, hypothesis testing
@article{AIHPB_2011__47_4_1219_0,
     author = {Morvai, Guszt\'av and Weiss, Benjamin},
     title = {Testing stationary processes for independence},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1219--1225},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {4},
     year = {2011},
     doi = {10.1214/11-AIHP426},
     zbl = {1271.62196},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1214/11-AIHP426/}
}
TY  - JOUR
AU  - Morvai, Gusztáv
AU  - Weiss, Benjamin
TI  - Testing stationary processes for independence
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2011
SP  - 1219
EP  - 1225
VL  - 47
IS  - 4
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/articles/10.1214/11-AIHP426/
DO  - 10.1214/11-AIHP426
LA  - en
ID  - AIHPB_2011__47_4_1219_0
ER  - 
%0 Journal Article
%A Morvai, Gusztáv
%A Weiss, Benjamin
%T Testing stationary processes for independence
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2011
%P 1219-1225
%V 47
%N 4
%I Gauthier-Villars
%U http://archive.numdam.org/articles/10.1214/11-AIHP426/
%R 10.1214/11-AIHP426
%G en
%F AIHPB_2011__47_4_1219_0
Morvai, Gusztáv; Weiss, Benjamin. Testing stationary processes for independence. Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 4, pp. 1219-1225. doi : 10.1214/11-AIHP426. http://archive.numdam.org/articles/10.1214/11-AIHP426/

[1] D. H. Bailey. Sequential schemes for classifying and predicting ergodic processes. Ph.D. thesis, Stanford Univ., 1976. | MR

[2] A. Berger. On uniformly consistent tests. Ann. Math. Statist. 22 (1951) 289-293. | MR | Zbl

[3] A. Dembo and Y. Peres. A topological criterion for hypothesis testing. Ann. Statist. 22 (1994) 106-117. | MR | Zbl

[4] W. Hoeffding. Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 (1963) 13-30. | MR | Zbl

[5] W. Hoeffding and J. Wolfowitz. Distinguishability of sets of distributions. Ann. Math. Statist. 29 (1958) 700-718. | MR | Zbl

[6] Ch. Kraft. Some conditions for consistency and uniform consistency of statistical procedures. Univ. California Publ. Statist. 2 (1955) 125-141. | MR | Zbl

[7] G. Morvai and B. Weiss. Order estimation of Markov chains. IEEE Trans. Inform. Theory 51 (2005) 1496-1497. | MR

[8] G. Morvai and B. Weiss. On classifying processes. Bernoulli 11 (2005) 523-532. | MR | Zbl

[9] G. Morvai and B. Weiss. Estimating the lengths of memory words. IEEE Transactions on Information Theory 54 (2008) 3804-3807. | MR

[10] A. Nobel. Hypothesis testing for families of ergodic processes. Bernoulli 12 (2006) 251-269. | MR | Zbl

[11] D. Ornstein and B. Weiss. How sampling reveals a process. Ann. Probab. 18 (1990) 905-930. | MR | Zbl

[12] B. Weiss. Some remarks on filtering and prediction of stationary processes. Israel J. Math. 149 (2005) 345-360. | MR | Zbl

Cité par Sources :