A versatile scheme for predicting renewal times

Gusztáv Morvai; Benjamin Weiss

Kybernetika (2016)

  • Volume: 52, Issue: 3, page 348-358
  • ISSN: 0023-5954

Abstract

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There are two kinds of universal schemes for estimating residual waiting times, those where the error tends to zero almost surely and those where the error tends to zero in some integral norm. Usually these schemes are different because different methods are used to prove their consistency. In this note we will give a single scheme where the average error is eventually small for all time instants, while the error itself tends to zero along a sequence of stopping times of density one.

How to cite

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Morvai, Gusztáv, and Weiss, Benjamin. "A versatile scheme for predicting renewal times." Kybernetika 52.3 (2016): 348-358. <http://eudml.org/doc/281541>.

@article{Morvai2016,
abstract = {There are two kinds of universal schemes for estimating residual waiting times, those where the error tends to zero almost surely and those where the error tends to zero in some integral norm. Usually these schemes are different because different methods are used to prove their consistency. In this note we will give a single scheme where the average error is eventually small for all time instants, while the error itself tends to zero along a sequence of stopping times of density one.},
author = {Morvai, Gusztáv, Weiss, Benjamin},
journal = {Kybernetika},
keywords = {nonparametric estimation; stationary processes},
language = {eng},
number = {3},
pages = {348-358},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A versatile scheme for predicting renewal times},
url = {http://eudml.org/doc/281541},
volume = {52},
year = {2016},
}

TY - JOUR
AU - Morvai, Gusztáv
AU - Weiss, Benjamin
TI - A versatile scheme for predicting renewal times
JO - Kybernetika
PY - 2016
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 3
SP - 348
EP - 358
AB - There are two kinds of universal schemes for estimating residual waiting times, those where the error tends to zero almost surely and those where the error tends to zero in some integral norm. Usually these schemes are different because different methods are used to prove their consistency. In this note we will give a single scheme where the average error is eventually small for all time instants, while the error itself tends to zero along a sequence of stopping times of density one.
LA - eng
KW - nonparametric estimation; stationary processes
UR - http://eudml.org/doc/281541
ER -

References

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  8. Morvai, G., Weiss, B., 10.1214/07-aap512, Ann. Appl. Probab. 18 (2008), 5, 1970-1992. Zbl1158.62053MR2462556DOI10.1214/07-aap512
  9. Morvai, G., Weiss, B., 10.1109/itwnit.2009.5158543, In: Proceedings of ITW2009, Volos 2009, pp. 67-70. DOI10.1109/itwnit.2009.5158543
  10. Morvai, G., Weiss, B., 10.1109/tit.2013.2268913, IEEE Trans. Inform. Theory 59 (2013), 6873-6879. MR3106870DOI10.1109/tit.2013.2268913
  11. Morvai, G., Weiss, B., 10.14736/kyb-2014-6-0869, Kybernetika 50 (2014), 869-882. Zbl1308.62067MR3301776DOI10.14736/kyb-2014-6-0869
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