The Annals of Statistics
- Ann. Statist.
- Volume 12, Number 4 (1984), 1434-1447.
Estimation of a Noisy Discrete-Time Step Function: Bayes and Empirical Bayes Approaches
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.
Ann. Statist., Volume 12, Number 4 (1984), 1434-1447.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
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
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. https://projecteuclid.org/euclid.aos/1176346802