The Annals of Statistics

Estimation of a Noisy Discrete-Time Step Function: Bayes and Empirical Bayes Approaches

Yi-Ching Yao

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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.

Article information

Ann. Statist., Volume 12, Number 4 (1984), 1434-1447.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]
Secondary: 93E14: Data smoothing 62G05: Estimation 62C12: Empirical decision procedures; empirical Bayes procedures

Change points Bayes empirical Bayes filtering smoothing


Yao, Yi-Ching. Estimation of a Noisy Discrete-Time Step Function: Bayes and Empirical Bayes Approaches. Ann. Statist. 12 (1984), no. 4, 1434--1447. doi:10.1214/aos/1176346802.

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