Multi-stage procedures for the minimum risk and bounded risk point estimation of the location of negative exponential distribution under the modified LINEX loss function

Abstract

In this paper, we develop purely sequential, two-stage, three-stage, and “accelerated” sequential procedures for the point estimation of the location of negative exponential distribution having an unknown scale parameter. We do minimum risk point estimation by using all four sequential procedures mentioned above. In addition, we do bounded risk point estimation by using three-stage and “accelerated” sequential procedures. Consideration is given to a modified LINEX loss function. We aim at controlling the associated risk functions for all the procedures. Second-order approximations are obtained for the proposed procedures. We also discuss first-order properties for purely sequential procedure.

Keywords:

• “Accelerated”
• bounded risk
• first-order properties
• LINEX loss
• minimum risk
• negative exponential
• point estimation
• purely sequential
• “regret”
• risk per unit cost
• second-order approximations
• three-stage
• two-stage

MATHEMATICS SUBJECT CLASSIFICATION:

• 62L05
• 62L12
• 62F10
• 62G20