Testing stationary processes for independence

Gusztáv Morvai; Benjamin Weiss

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 4, page 1219-1225
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Morvai, Gusztáv, and Weiss, Benjamin. "Testing stationary processes for independence." Annales de l'I.H.P. Probabilités et statistiques 47.4 (2011): 1219-1225. <http://eudml.org/doc/242237>.

@article{Morvai2011,
abstract = {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.},
author = {Morvai, Gusztáv, Weiss, Benjamin},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {independent processes; hypothesis testing},
language = {eng},
number = {4},
pages = {1219-1225},
publisher = {Gauthier-Villars},
title = {Testing stationary processes for independence},
url = {http://eudml.org/doc/242237},
volume = {47},
year = {2011},
}

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
PB - Gauthier-Villars
VL - 47
IS - 4
SP - 1219
EP - 1225
AB - 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.
LA - eng
KW - independent processes; hypothesis testing
UR - http://eudml.org/doc/242237
ER -

References

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  1. [1] D. H. Bailey. Sequential schemes for classifying and predicting ergodic processes. Ph.D. thesis, Stanford Univ., 1976. MR2626644
  2. [2] A. Berger. On uniformly consistent tests. Ann. Math. Statist. 22 (1951) 289–293. Zbl0042.38003MR42653
  3. [3] A. Dembo and Y. Peres. A topological criterion for hypothesis testing. Ann. Statist. 22 (1994) 106–117. Zbl0818.62010MR1272078
  4. [4] W. Hoeffding. Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 (1963) 13–30. Zbl0127.10602MR144363
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  6. [6] Ch. Kraft. Some conditions for consistency and uniform consistency of statistical procedures. Univ. California Publ. Statist. 2 (1955) 125–141. Zbl0066.12202MR73896
  7. [7] G. Morvai and B. Weiss. Order estimation of Markov chains. IEEE Trans. Inform. Theory 51 (2005) 1496–1497. Zbl1309.62144MR2241507
  8. [8] G. Morvai and B. Weiss. On classifying processes. Bernoulli 11 (2005) 523–532. Zbl1073.62077MR2146893
  9. [9] G. Morvai and B. Weiss. Estimating the lengths of memory words. IEEE Transactions on Information Theory 54 (2008) 3804–3807. Zbl1329.60095MR2451043
  10. [10] A. Nobel. Hypothesis testing for families of ergodic processes. Bernoulli 12 (2006) 251–269. Zbl1099.62097MR2218555
  11. [11] D. Ornstein and B. Weiss. How sampling reveals a process. Ann. Probab. 18 (1990) 905–930. Zbl0709.60036MR1062052
  12. [12] B. Weiss. Some remarks on filtering and prediction of stationary processes. Israel J. Math. 149 (2005) 345–360. Zbl1085.60024MR2191220

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