On universal estimates for binary renewal processes

G. Morvai, Benjamin Weiss

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A binary 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. After observing X 1, . . . , X n 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.

Original languageEnglish
Pages (from-to)1970-1992
Number of pages23
JournalAnnals of Applied Probability
Volume18
Issue number5
DOIs
Publication statusPublished - Oct 2008

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Renewal Process
Renewal
Moment Conditions
Binary
Estimate
Conditional Distribution
Prior Knowledge
Stochastic Processes
Estimator
Predict
Necessary
Zero
Renewal process
Moment conditions

Keywords

  • Prediction theory
  • Renewal theory

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

On universal estimates for binary renewal processes. / Morvai, G.; Weiss, Benjamin.

In: Annals of Applied Probability, Vol. 18, No. 5, 10.2008, p. 1970-1992.

Research output: Contribution to journalArticle

Morvai, G. ; Weiss, Benjamin. / On universal estimates for binary renewal processes. In: Annals of Applied Probability. 2008 ; Vol. 18, No. 5. pp. 1970-1992.
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