On universal estimates for binary renewal processes
Gusztáv Morvai,Benjamin Weiss +1 more
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In this article, the authors prove universal estimates for the expected time to renewal as well as the conditional distribution of the time-to-renewal distribution of a binary renewal process.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 ${X_0,X_1,...,X_n}$ 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.read more
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Journal ArticleDOI
Long-Term Prediction Intervals of Time Series
Zhou Zhou,Zhiwei Xu,Wei Biao Wu +2 more
TL;DR: In contrast with the conventional prediction problem in which one predicts a future value given past values of the process, in this setting the number of aggregates can go to infinity with respect to thenumber of available observations.
Journal ArticleDOI
On universal algorithms for classifying and predicting stationary processes
Gusztáv Morvai,Benjamin Weiss +1 more
TL;DR: This is a survey of results on universal algorithms for classification and prediction of stationary processes and the forward and the backward prediction problems are discussed with the emphasis being on pointwise results.
Proceedings ArticleDOI
Estimating the residual waiting time for binary stationary time series
Gusztáv Morvai,Benjamin Weiss +1 more
TL;DR: A universal estimation scheme for the problem of estimating the residual waiting time until the next occurrence of a zero after observing the first n outputs of a stationary and ergodic binary process is presented.
Journal ArticleDOI
Universal rates for estimating the residual waiting time in an intermittent way
Gusztáv Morvai,Benjamin P. Weiss +1 more
Journal ArticleDOI
A versatile scheme for predicting renewal times
Gusztáv Morvai,Benjamin Weiss +1 more
TL;DR: This note gives a single scheme where the average error is eventually small for all time instants, while the error itself tends to zero along a sequence of stopping times of density one.
References
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An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
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TL;DR: In this article, the B-processes Bibliography index is used to find entropy-related properties for restricted classes of B-Processes, including entropy related properties and properties.
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TL;DR: In this article, it was shown that (4) is not generally true with $C(r, n) = 1$ even when r.v.'s are independent and have zero means.
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Single Orbit Dynamics
TL;DR: In this paper, the authors define single orbit dynamics topological and topological dynamics, ergodicity and unique Ergodicity Ergodic and uniquely ergodic orbits Translation invariant graphs and recurrence patterns in large sets Entropy and disjointness.