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December, 1984 Estimation of a Noisy Discrete-Time Step Function: Bayes and Empirical Bayes Approaches
Yi-Ching Yao
Ann. Statist. 12(4): 1434-1447 (December, 1984). DOI: 10.1214/aos/1176346802


Consider the problem of estimating, in a Bayesian framework and in the presence of additive Gaussian noise, a signal which is a step function. Best linear estimates and Bayes estimates are derived, evaluated and compared. A characterization of the Bayes estimates is presented. This characterization has an intuitive interpretation and also provides a way to compute the Bayes estimates with a number of operations of the order of $T^3$ where $T$ is the fixed time span. An approximation to the Bayes estimates is proposed which reduces the total number of operations to the order of $T$. The results are applied to the case where the Bayesian model fails to be satisfied using an empirical Bayes approach.


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Yi-Ching Yao. "Estimation of a Noisy Discrete-Time Step Function: Bayes and Empirical Bayes Approaches." Ann. Statist. 12 (4) 1434 - 1447, December, 1984.


Published: December, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0551.62069
MathSciNet: MR760698
Digital Object Identifier: 10.1214/aos/1176346802

Primary: 62M20
Secondary: 62C12 , 62G05 , 93E14

Keywords: Bayes , Change points , Empirical Bayes , Filtering , smoothing

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 4 • December, 1984
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