## The Annals of Statistics

- Ann. Statist.
- Volume 5, Number 5 (1977), 955-968.

### Bayesian Sequential Estimation

#### 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 $c$.

#### Article information

**Source**

Ann. Statist., Volume 5, Number 5 (1977), 955-968.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343951

**Digital Object Identifier**

doi:10.1214/aos/1176343951

**Mathematical Reviews number (MathSciNet)**

MR448751

**Zentralblatt MATH identifier**

0368.62061

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62L12: Sequential estimation

Secondary: 62C10: Bayesian problems; characterization of Bayes procedures

**Keywords**

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

#### Citation

Alvo, Mayer. Bayesian Sequential Estimation. Ann. Statist. 5 (1977), no. 5, 955--968. doi:10.1214/aos/1176343951. https://projecteuclid.org/euclid.aos/1176343951