## The Annals of Statistics

### Bayesian Sequential Estimation

Mayer Alvo

#### 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

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