Bernoulli

  • Bernoulli
  • Volume 11, Number 3 (2005), 523-532.

On classifying processes

Gusztáv Morvai and Benjamin Weiss

Full-text: Open access

Abstract

We prove several results concerning classifications, based on successive observations (X1, ..., Xn) of an unknown stationary and ergodic process, for membership of a given class of processes, such as the class of all finite-order Markov chains.

Article information

Source
Bernoulli, Volume 11, Number 3 (2005), 523-532.

Dates
First available in Project Euclid: 5 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.bj/1120591187

Digital Object Identifier
doi:10.3150/bj/1120591187

Mathematical Reviews number (MathSciNet)
MR2146893

Zentralblatt MATH identifier
1073.62077

Keywords
nonparametric classification stationary and ergodic processes

Citation

Morvai, Gusztáv; Weiss, Benjamin. On classifying processes. Bernoulli 11 (2005), no. 3, 523--532. doi:10.3150/bj/1120591187. https://projecteuclid.org/euclid.bj/1120591187


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References

  • [1] Bailey, D.H. (1976) Sequential schemes for classifying and predicting ergodic processes. Ph.D. thesis, Stanford University.
  • [2] Cornfeld, I.P., Fomin, S.F. and Sinai, Ya.G. (1982) Ergodic Theory. New York: Springer-Verlag.
  • [3] Csiszár, I. and Shields, P. (2000) The consistency of the BIC Markov order estimator. Ann. Statist., 28, 1601-1619.
  • [4] Gray, R.M. (1988) Probability, Random Processes, and Ergodic Properties. New York: Springer- Verlag.
  • [5] Györfi, L., Morvai, G. and Yakowitz, S. (1998) Limits to consistent on-line forecasting for ergodic time series. IEEE Trans. Inform. Theory, 44, 886-892.
  • [6] Kalikow, S., Katznelson, Y. and Weiss, B. (1992) Finitarily deterministic generators for zero entropy systems. Israel J. Math., 79, 33-45.
  • [7] Kemeny, J.G. and Snell, J.L. (1960) Finite Markov Chains. Princeton, NJ: Van Nostrand Reinhold.
  • [8] Morvai, G. (2003) Guessing the output of a stationary binary time series. In Y. Haitovsky, H.R. Lerche and Y. Ritov (eds), Foundations of Statistical Inference, pp. 207-215. Heidelberg: Physica-Verlag.
  • [9] Morvai, G. and Weiss, B. (2003) Forecasting for stationary binary time series. Acta Appl. Math., 79, 25-34.
  • [10] Ornstein, D. and Weiss, B. (1990) How sampling reveals a process. Ann Probab., 18, 905-930.
  • [11] Shields, P.C. (1996) The Ergodic Theory of Discrete Sample Paths. Providence, RI: American Mathematical Society.