The Information Inequality in Sequential Estimation for the Uniform Case

Abstract

We consider sequential estimation of a parameter based on the independent and identically distributed sample from the uniform distribution with range 1. The optimal sequential estimation procedure in the sense of minimizing the Bayes risk with respect to the uniform prior distribution is obtained, from which the information inequality derived. A comparison between the sequential and nonsequential cases is also given.

Keywords:

• Uniform distributions
• Sequential estimation procedure
• Bayes risk
• Prior distribution
• Posterior distribution
• Stopping timer
• Information inequality

Acknowledgment

The authors wish to thank the referee for the kind comments.