Inferring the residual waiting time for binary stationary time series

Gusztáv Morvai; Benjamin Weiss

Kybernetika (2014)

  • Volume: 50, Issue: 6, page 869-882
  • ISSN: 0023-5954

Abstract

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For a binary stationary time series define σ n to be the number of consecutive ones up to the first zero encountered after time n , and consider the problem of estimating the conditional distribution and conditional expectation of σ n after one has observed the first n outputs. We present a sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes. In case the process is a renewal process with zero the renewal state the stopping times along which we estimate have density one.

How to cite

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Morvai, Gusztáv, and Weiss, Benjamin. "Inferring the residual waiting time for binary stationary time series." Kybernetika 50.6 (2014): 869-882. <http://eudml.org/doc/262142>.

@article{Morvai2014,
abstract = {For a binary stationary time series define $\sigma _n$ to be the number of consecutive ones up to the first zero encountered after time $n$, and consider the problem of estimating the conditional distribution and conditional expectation of $\sigma _n$ after one has observed the first $n$ outputs. We present a sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes. In case the process is a renewal process with zero the renewal state the stopping times along which we estimate have density one.},
author = {Morvai, Gusztáv, Weiss, Benjamin},
journal = {Kybernetika},
keywords = {nonparametric estimation; stationary processes; nonparametric estimation; stationary processes},
language = {eng},
number = {6},
pages = {869-882},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Inferring the residual waiting time for binary stationary time series},
url = {http://eudml.org/doc/262142},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Morvai, Gusztáv
AU - Weiss, Benjamin
TI - Inferring the residual waiting time for binary stationary time series
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 6
SP - 869
EP - 882
AB - For a binary stationary time series define $\sigma _n$ to be the number of consecutive ones up to the first zero encountered after time $n$, and consider the problem of estimating the conditional distribution and conditional expectation of $\sigma _n$ after one has observed the first $n$ outputs. We present a sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes. In case the process is a renewal process with zero the renewal state the stopping times along which we estimate have density one.
LA - eng
KW - nonparametric estimation; stationary processes; nonparametric estimation; stationary processes
UR - http://eudml.org/doc/262142
ER -

References

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  1. Algoet, P., 10.1109/18.761258, IEEE Trans. Inform. Theory 45 (1999), 1165-1185. Zbl0959.62078MR1686250DOI10.1109/18.761258
  2. Bailey, D. H., Sequential Schemes for Classifying and Predicting Ergodic Processes., Ph. D. Thesis, Stanford University 1976. MR2626644
  3. Bunea, F., Nobel, A., 10.1109/TIT.2008.917657, IEEE Trans. Inform. Theory 54 (2008), 4, 1725-1735. MR2450298DOI10.1109/TIT.2008.917657
  4. Feller, W., An Introduction to Probability Theory and its Applications. Vol. II. Second edition., John Wiley and Sons, New York - London - Sydney 1971. MR0270403
  5. Györfi, L., Morvai, G., Yakowitz, S., 10.1109/18.661540, IEEE Trans. Inform. Theory 44 (1998), 886-892. Zbl0899.62122MR1607704DOI10.1109/18.661540
  6. Morvai, G., Weiss, B., Inferring the conditional mean., Theory Stoch. Process. 11 (2005), 112-120. Zbl1164.62382MR2327452
  7. Morvai, G., Weiss, B., 10.1109/TIT.2005.844093, IEEE Trans. Inform. Theory 51 (2005), 1496-1497. MR2241507DOI10.1109/TIT.2005.844093
  8. Morvai, G., Weiss, B., 10.1142/S021949370700213X, Stoch. Dyn. 7 (2007), 4, 417-437. Zbl1255.62228MR2378577DOI10.1142/S021949370700213X
  9. Morvai, G., Weiss, B., 10.1214/07-AAP512, Ann. Appl. Probab. 18 (2008), 5, 1970-1992. Zbl1158.62053MR2462556DOI10.1214/07-AAP512
  10. Morvai, G., Weiss, B., Estimating the residual waiting time for binary stationary time series., In: Proc. ITW2009, Volos 2009, pp. 67-70. 
  11. Morvai, G., Weiss, B., A note on prediction for discrete time series., Kybernetika 48 (2012), 4, 809-823. MR3013400
  12. Ryabko, B. Ya., Prediction of random sequences and universal coding., Probl. Inf. Trans. 24 (1988), 87-96. Zbl0666.94009MR0955983
  13. Ryabko, D., Ryabko, B., 10.1109/TIT.2009.2039169, IEEE Trans. Inform. Theory 56 (2010), 3, 1430-1435. MR2723689DOI10.1109/TIT.2009.2039169
  14. Shiryayev, A. N., Probability., Springer-Verlag, New York 1984. MR0737192
  15. Takahashi, H., 10.1109/TIT.2011.2165791, IEEE Trans. Inform. Theory 57 (2011), 10, 6995-6999. MR2882275DOI10.1109/TIT.2011.2165791
  16. Zhou, Z., Xu, Z., Wu, W. B., 10.1109/TIT.2009.2039158, IEEE Trans. Inform. Theory 56 (2010), 3, 1436-1446. MR2723690DOI10.1109/TIT.2009.2039158

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