Universal rates for estimating the residual waiting time in an intermittent way

Gusztáv Morvai; Benjamin Weiss

Kybernetika (2020)

  • Volume: 56, Issue: 4, page 601-616
  • ISSN: 0023-5954

Abstract

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A simple renewal process is a stochastic process { X n } taking values in { 0 , 1 } where the lengths of the runs of 1 ’s between successive zeros are independent and identically distributed. After observing X 0 , X 1 , ... X n one would like to estimate the time remaining until the next occurrence of a zero, and the problem of universal estimators is to do so without prior knowledge of the distribution of the process. We give some universal estimates with rates for the expected time to renewal as well as for the conditional distribution of the time to renewal.

How to cite

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Morvai, Gusztáv, and Weiss, Benjamin. "Universal rates for estimating the residual waiting time in an intermittent way." Kybernetika 56.4 (2020): 601-616. <http://eudml.org/doc/297351>.

@article{Morvai2020,
abstract = {A simple renewal process is a stochastic process $\lbrace X_n\rbrace $ taking values in $\lbrace 0,1\rbrace $ where the lengths of the runs of $1$’s between successive zeros are independent and identically distributed. After observing $\{X_0, X_1, \ldots X_n\}$ one would like to estimate the time remaining until the next occurrence of a zero, and the problem of universal estimators is to do so without prior knowledge of the distribution of the process. We give some universal estimates with rates for the expected time to renewal as well as for the conditional distribution of the time to renewal.},
author = {Morvai, Gusztáv, Weiss, Benjamin},
journal = {Kybernetika},
keywords = {statistical learning; statistical inference; prediction methods; renewal theory},
language = {eng},
number = {4},
pages = {601-616},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Universal rates for estimating the residual waiting time in an intermittent way},
url = {http://eudml.org/doc/297351},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Morvai, Gusztáv
AU - Weiss, Benjamin
TI - Universal rates for estimating the residual waiting time in an intermittent way
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 4
SP - 601
EP - 616
AB - A simple renewal process is a stochastic process $\lbrace X_n\rbrace $ taking values in $\lbrace 0,1\rbrace $ where the lengths of the runs of $1$’s between successive zeros are independent and identically distributed. After observing ${X_0, X_1, \ldots X_n}$ one would like to estimate the time remaining until the next occurrence of a zero, and the problem of universal estimators is to do so without prior knowledge of the distribution of the process. We give some universal estimates with rates for the expected time to renewal as well as for the conditional distribution of the time to renewal.
LA - eng
KW - statistical learning; statistical inference; prediction methods; renewal theory
UR - http://eudml.org/doc/297351
ER -

References

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