Asymptotic Non-Deficiency of Some Procedures for a Particular Exponential Family Under Relative LINEX Loss

Abstract

The problem of Bayes sequential estimation of the unknown parameter in a particular exponential family of distributions with relative LINEX loss and fixed cost for each observation is considered in this article. Optimal, nearly optimal, and asymptotically pointwise optimal procedures with deterministic stopping rules are derived, and the approximate optimal procedures are shown to be asymptotically nondeficient in the sense of Woodroofe (1981). In addition, a robust procedure with a deterministic stopping rule, which does not depend on the parameters of the prior distribution, is proposed, and the asymptotic second-order expansion of the corresponding Bayes risk is obtained.

Keywords:

• Asymptotically nondeficient
• Asymptotically optimal
• Asymptotically pointwise optimal
• Deterministic stopping rule
• Optimal procedure
• Relative LINEX loss
• Robust

Subject Classifications:

• 62L12
• 62C10

Notes

Recommended by S. Chattopadhyay