Geodesic
Universal rates for estimating the residual waiting time in an intermittent way
Kybernetika, Tome 56 (2020) no. 4, pp. 601-616 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 ${X_0, X_1, \ldots X_n}$ 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.
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 ${X_0, X_1, \ldots X_n}$ 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.
DOI : 10.14736/kyb-2020-4-0601
Classification : 60G25, 60K05
Keywords: statistical learning; statistical inference; prediction methods; renewal theory 
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Morvai, Gusztáv; Weiss, Benjamin. Universal rates for estimating the residual waiting time in an intermittent way. Kybernetika, Tome 56 (2020) no. 4, pp. 601-616. doi: 10.14736/kyb-2020-4-0601

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