ON UNIVERSAL ESTIMATES FOR BINARY RENEWAL PROCESSES

• 成果类型: Article
• 署名作者: Morvai, Gusztav; Weiss, Benjamin
• 署名单位: MTA-BME Stochastics Research Group; Hebrew University of Jerusalem
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP512
• 发表日期: 2008
• 页码: 1970-1992
• 关键词: stationary time-series; prediction; schemes; output; LIMITS

摘要

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-0, 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.