## The Annals of Statistics

### A Bayesian Approach to a Problem in Sequential Estimation

Shelley L. Rasmussen

#### Abstract

This paper considers the problem of sequentially estimating the mean of a normal distribution when the variance is unknown. A continuous time analogue of the discrete time problem is studied. For $L$ in a class of loss functions, properties of the value function and optimal continuation region of $L$ are presented. Asymptotic expansions are found for the value function and the optimal boundary function of the loss function $L$.

#### Article information

Source
Ann. Statist., Volume 8, Number 6 (1980), 1229-1243.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345196

Digital Object Identifier
doi:10.1214/aos/1176345196

Mathematical Reviews number (MathSciNet)
MR594640

Zentralblatt MATH identifier
0454.62076

JSTOR