Multistage Estimation Procedures with Bounded Risk for the Normal Mean Under LINEX Loss Function

Abstract

This paper considers multistage estimation procedures to achieve a bounded risk when estimating the mean of a normal distribution under a LINEX loss function. Two-stage and three-stage estimation procedures are introduced and their second-order asymptotics are examined. Moderate-sample-size performances are compared between multistage and purely sequential procedures.

Recommended by Saibal Chattopadhyay

Keywords:

• Bounded risk problem
• LINEX loss function
• Second-order asymptotics
• Three-stage procedure
• Two-stage procedure

Subject Classifications:

• 62L10
• 62L12

ACKNOWLEDGMENTS

The author wishes to thank Professor Nitis Mukhopadhyay for valuable suggestions. This research was supported by Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture, Japan, under Contract Number 15500188.

Notes

Recommended by Saibal Chattopadhyay