The Annals of Statistics

A Bayesian Approach to a Problem in Sequential Estimation

Shelley L. Rasmussen

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62L12: Sequential estimation
Secondary: 62F10: Point estimation 62L15: Optimal stopping [See also 60G40, 91A60] 60J25: Continuous-time Markov processes on general state spaces 60J30 62F15: Bayesian inference

Keywords
Bayesian sequential estimation normal distribution gamma distribution normal-gamma prior distribution loss function value function optimal continuation region optimal stopping rule asymptotic approximations

Citation

Rasmussen, Shelley L. A Bayesian Approach to a Problem in Sequential Estimation. Ann. Statist. 8 (1980), no. 6, 1229--1243. doi:10.1214/aos/1176345196. https://projecteuclid.org/euclid.aos/1176345196


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