Bayes Sequential Estimation for One-Parameter Exponential Family Under Asymmetric LINEX Loss Function

Abstract

The problem of Bayes sequential estimation of the mean in one-parameter exponential family with LINEX (linear-exponential) loss function and fixed cost for each observation is considered in this article. Given a prior, a family of stopping times is proposed and shown to be asymptotically pointwise optimal and asymptotically optimal. In addition, we propose a robust sequential procedure, not depending on the distribution of outcome variables and the prior. It is shown that the procedure also shares the asymptotic properties with the asymptotically pointwise optimal rules for a large class of prior distributions.

Keywords:

• Asymptotically optimal
• Asymptotically pointwise optimal
• Prior distribution
• Robust sequential procedure
• Uniform integrability

Subject Classifications:

• 62L12
• 62C10

ACKNOWLEDGMENT

This research was supported by the National Science Council of R.O.C. The authors thank the Associate Editor and a referee for several helpful comments.

Notes

Recommended by Ben Boukai