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September, 1977 Bayesian Sequential Estimation
Mayer Alvo
Ann. Statist. 5(5): 955-968 (September, 1977). DOI: 10.1214/aos/1176343951

Abstract

For fixed $\theta$, let $X_1, X_2, \cdots$ be a sequence of independent identically distributed random variables having density $f_\theta(x)$. Using a sequential Bayes decision theoretic approach we consider the problem of estimating any strictly monotone function $g(\theta)$ when the error incurred by a wrong estimate is measured by squared error loss and the sampling cost is $c$ units per observation. A heuristic stopping rule is suggested. It is shown that the excess risk which results when using it is bounded above by terms of order $c$.

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Mayer Alvo. "Bayesian Sequential Estimation." Ann. Statist. 5 (5) 955 - 968, September, 1977. https://doi.org/10.1214/aos/1176343951

Information

Published: September, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0368.62061
MathSciNet: MR448751
Digital Object Identifier: 10.1214/aos/1176343951

Subjects:
Primary: 62L12
Secondary: 62C10

Keywords: asymptotic expansion , Bayesian sequential estimation , lower bound , martingale , risk , stopping rule , upper bound

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 5 • September, 1977
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