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October 2008 On universal estimates for binary renewal processes
Gusztáv Morvai, Benjamin Weiss
Ann. Appl. Probab. 18(5): 1970-1992 (October 2008). DOI: 10.1214/07-AAP512

Abstract

A binary renewal process is a stochastic process {Xn} taking values in {0, 1} where the lengths of the runs of 1’s between successive zeros are independent. After observing X0, X1, …, Xn one would like to predict the future behavior, and the problem of universal estimators is to do so without any prior knowledge of the distribution. We prove a variety of results of this type, including universal estimates for the expected time to renewal as well as estimates for the conditional distribution of the time to renewal. Some of our results require a moment condition on the time to renewal and we show by an explicit construction how some moment condition is necessary.

Citation

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Gusztáv Morvai. Benjamin Weiss. "On universal estimates for binary renewal processes." Ann. Appl. Probab. 18 (5) 1970 - 1992, October 2008. https://doi.org/10.1214/07-AAP512

Information

Published: October 2008
First available in Project Euclid: 30 October 2008

zbMATH: 1158.62053
MathSciNet: MR2462556
Digital Object Identifier: 10.1214/07-AAP512

Subjects:
Primary: 60G25, 60K05

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.18 • No. 5 • October 2008
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