Sequential minimum risk point estimation (MRPE) methodology for a normal mean under Linex loss plus sampling cost: First-order and second-order asymptotics

Abstract

We have designed a sequential minimum risk point estimation (MRPE) strategy for the unknown mean of a normal population having its variance unknown too. This is developed under a Linex loss plus linear cost of sampling. A number of important asymptotic first-order and asymptotic second-order properties' characteristics have been developed and proved thoroughly. Extensive sets of simulations tend to validate nearly all of these asymptotic properties for small to medium to large optimal fixed sample sizes.

Keywords:

• First-order properties
• linear cost
• Linex loss
• minimum risk
• nonlinear renewal theory
• regret
• risk efficiency
• second-order properties
• sequential
• simulations

Subject Classifications::

• 62L12
• 62L10
• 62L05

Acknowledgment

An Associate Editor and the reviewers shared helpful comments with us. We heartily thank them.