On Universal Estimates for Binary Renewal Processes

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 X₀, X₁,..., $X_{n}$ one would like to predict the future behavior, and the problem of universal estimators is to do...

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:	The Annals of Applied Probability. - Institute of Mathematical Statistics. - 18(2008), 5, Seite 1970-1992
1. Verfasser:	Morvai, Gusztáv (VerfasserIn)
Weitere Verfasser:	Weiss, Benjamin
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2008
Zugriff auf das übergeordnete Werk:	The Annals of Applied Probability
Schlagworte:	Prediction theory Renewal theory Mathematics Applied sciences Physical sciences Information science


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520			\|a 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 X₀, X₁,..., $X_{n}$ 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.
540			\|a Copyright 2008 The Institute of Mathematical Statistics
650		4	\|a Prediction theory
650		4	\|a Renewal theory
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Inferential statistics \|x Statistical estimation \|x Estimation methods \|x Estimators
650		4	\|a Applied sciences \|x Engineering \|x Automotive engineering \|x Stopping power \|x Stopping distances
650		4	\|a Applied sciences \|x Systems science \|x Systems theory \|x Dynamical systems \|x Ergodic theory
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Markov processes \|x Markov chains
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Density \|x Density measurement \|x Density estimation
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Descriptive statistics \|x Statistical distributions \|x Distribution functions \|x Probability distributions \|x Mathematical moments
650		4	\|a Information science \|x Information analysis \|x Data analysis \|x Time series analysis \|x Time series forecasting
650		4	\|a Mathematics \|x Pure mathematics \|x Discrete mathematics \|x Number theory \|x Numbers \|x Real numbers \|x Rational numbers \|x Integers \|x Zero
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Inferential statistics \|x Statistical estimation \|x Estimation methods \|x Estimators
650		4	\|a Applied sciences \|x Engineering \|x Automotive engineering \|x Stopping power \|x Stopping distances
650		4	\|a Applied sciences \|x Systems science \|x Systems theory \|x Dynamical systems \|x Ergodic theory
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Markov processes \|x Markov chains
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Density \|x Density measurement \|x Density estimation
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Descriptive statistics \|x Statistical distributions \|x Distribution functions \|x Probability distributions \|x Mathematical moments
650		4	\|a Information science \|x Information analysis \|x Data analysis \|x Time series analysis \|x Time series forecasting
650		4	\|a Mathematics \|x Pure mathematics \|x Discrete mathematics \|x Number theory \|x Numbers \|x Real numbers \|x Rational numbers \|x Integers \|x Zero
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory
655		4	\|a research-article
700	1		\|a Weiss, Benjamin \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t The Annals of Applied Probability \|d Institute of Mathematical Statistics \|g 18(2008), 5, Seite 1970-1992 \|w (DE-627)270937838 \|w (DE-600)1478737-4 \|x 10505164 \|7 nnns
773	1	8	\|g volume:18 \|g year:2008 \|g number:5 \|g pages:1970-1992
856	4	0	\|u https://www.jstor.org/stable/25442700 \|3 Volltext
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