Intermittent estimation for finite alphabet finitarily Markovian processes with exponential tails

Gusztáv Morvai; Benjamin Weiss

Kybernetika (2021)

  • Volume: 57, Issue: 4, page 628-646
  • ISSN: 0023-5954

Abstract

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We give some estimation schemes for the conditional distribution and conditional expectation of the the next output following the observation of the first n outputs of a stationary process where the random variables may take finitely many possible values. Our schemes are universal in the class of finitarily Markovian processes that have an exponential rate for the tail of the look back time distribution. In addition explicit rates are given. A necessary restriction is that the scheme proposes an estimate only at certain stopping times, but these have density one so that one rarely fails to give an estimate.

How to cite

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Morvai, Gusztáv, and Weiss, Benjamin. "Intermittent estimation for finite alphabet finitarily Markovian processes with exponential tails." Kybernetika 57.4 (2021): 628-646. <http://eudml.org/doc/297569>.

@article{Morvai2021,
abstract = {We give some estimation schemes for the conditional distribution and conditional expectation of the the next output following the observation of the first $n$ outputs of a stationary process where the random variables may take finitely many possible values. Our schemes are universal in the class of finitarily Markovian processes that have an exponential rate for the tail of the look back time distribution. In addition explicit rates are given. A necessary restriction is that the scheme proposes an estimate only at certain stopping times, but these have density one so that one rarely fails to give an estimate.},
author = {Morvai, Gusztáv, Weiss, Benjamin},
journal = {Kybernetika},
keywords = {nonparametric estimation; stationary processes},
language = {eng},
number = {4},
pages = {628-646},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Intermittent estimation for finite alphabet finitarily Markovian processes with exponential tails},
url = {http://eudml.org/doc/297569},
volume = {57},
year = {2021},
}

TY - JOUR
AU - Morvai, Gusztáv
AU - Weiss, Benjamin
TI - Intermittent estimation for finite alphabet finitarily Markovian processes with exponential tails
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
VL - 57
IS - 4
SP - 628
EP - 646
AB - We give some estimation schemes for the conditional distribution and conditional expectation of the the next output following the observation of the first $n$ outputs of a stationary process where the random variables may take finitely many possible values. Our schemes are universal in the class of finitarily Markovian processes that have an exponential rate for the tail of the look back time distribution. In addition explicit rates are given. A necessary restriction is that the scheme proposes an estimate only at certain stopping times, but these have density one so that one rarely fails to give an estimate.
LA - eng
KW - nonparametric estimation; stationary processes
UR - http://eudml.org/doc/297569
ER -

References

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  1. Algoet, P., , IEEE Trans. Inform. Theory 40 (1994), 609-633. DOI
  2. Algoet, P., , IEEE Trans. Inform. Theory 45 (1999), 1165-1185. Zbl0959.62078DOI
  3. Bailey, D. H., Sequential Schemes for Classifying and Predicting Ergodic Processes., Ph.D. Thesis, Stanford University, 1976. 
  4. Csiszár, I., Talata, Zs., , IEEE Trans. Inform. Theory 52 (2006), 3, 1007-1016. DOI
  5. Györfi, L., Morvai, G., Yakowitz, S., , IEEE Trans. Inform. Theory 44 (1998), 886-892. Zbl0899.62122MR1607704DOI
  6. Hoeffding, W., 10.1080/01621459.1963.10500830, J. Amer. Statist. Assoc. 58 (1963), 13-30. DOI10.1080/01621459.1963.10500830
  7. Kalikow, S., Katznelson, Y., Weiss, B., , Israel J. Math. 79 (1992), 33-45. DOI
  8. Maker, Ph. T., The ergodic theorem for a sequence of functions., Duke Math. J. 6 (1940), 27-30. 
  9. Morvai, G., Guessing the output of a stationary binary time series., In: Foundations of Statistical Inference (Y. Haitovsky, H. R.Lerche, and Y. Ritov, eds.), Physika-Verlag, pp. 207-215, 2003. 
  10. Morvai, G., Yakowitz, S., Algoet, P., , IEEE Trans. Inform. Theory 43 (1997), 483-498. DOI
  11. Morvai, G., Weiss, B., , Acta Appl. Math. 79 (2003), 25-34. DOI
  12. Morvai, G., Weiss, B., , Test 13 (2004), 525-542. DOI
  13. Morvai, G., Weiss, B., Inferring the conditional mean., Theory Stochast. Process. 11 (2005), 1-2, 112-120. Zbl1164.62382
  14. Morvai, G., Weiss, B., , Probab. Theory Related Fields 132 (2005), 1-12. DOI
  15. Morvai, G., Weiss, B., , Statist. Probab. Lett. 72 (2005), 285-290. DOI
  16. Morvai, G., Weiss, B., , Bernoulli 11 (2005), 523-532. DOI
  17. Morvai, G., Weiss, B., , IEEE Trans. Inform. Theory 51 (2005), 1496-1497. DOI
  18. Morvai, G., Weiss, B., , Ann. I. H. Poincaré Probab. Statist. 41 (2005), 859-870. DOI
  19. Morvai, G., Weiss, B., , Ann. I. H. Poincaré PR 43 (2007), 15-30. DOI
  20. Morvai, G., Weiss, B., , Stoch. Dyn. 7 (2007), 4, 417-437. Zbl1255.62228DOI
  21. Morvai, G., Weiss, B., , IEEE Trans. Inform. Theory 54 (2008), 8, 3804-3807. Zbl1329.60095DOI
  22. Morvai, G., Weiss, B., , Annals Appl. Probab. 18 (2008), 5, 1970-1992. Zbl1158.62053DOI
  23. Morvai, G., Weiss, B., Estimating the residual waiting time for binary stationary time series., Proc. ITW2009, Volos 2009, pp. 67-70. 
  24. Morvai, G., Weiss, B., A note on prediction for discrete time series., Kybernetika 48 (2012), 4, 809-823. 
  25. Morvai, G., Weiss, B., , IEEE Trans. Inform. Theory 59 (2013), 6873-6879. DOI
  26. Morvai, G., Weiss, B., , Kybernetika 50 (2014), 869-882. Zbl1308.62067DOI
  27. Morvai, G., Weiss, B., , Kybernetika 52 (2016), 348-358. DOI
  28. Morvai, G., Weiss, B., , Kybernetika 56, (2020), 4, 601-616. DOI
  29. Morvai, G., Weiss, B., 10.1214/20-PS345, Probab. Surveys 18 (2021), 77-131. DOI10.1214/20-PS345
  30. Morvai, G., Weiss, B., , ALEA, Lat. Am. J. Probab. Math. Stat. 18 (2021), 1643-1667. DOI
  31. Ryabko, B. Ya., , Problems Inform. Trans. 24 (1988), 87-96. Zbl0666.94009DOI
  32. Ryabko, D., Asymptotic Nonparametric Statistical Analysis of Stationary Time Series., Springer, Cham 2019. 
  33. Shields, P. C., The Ergodic Theory of Discrete Sample Paths., In: Graduate Studies in Mathematics. American Mathematical Society 13, Providence 1996. Zbl0879.28031
  34. Suzuki, J., , Systems Computers Japan 34 (2003), 6, 1-11. DOI
  35. Takahashi, H., , IEEE Trans. Inform. Theory 57 (2011), 6995-6999. DOI

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