Sequential Estimation of the Powers of Normal and Exponential Scale Parameters

Abstract

We consider the bounded risk point estimation problem of the powers of a normal scale parameter and the problem of minimum risk point estimation of the powers of a negative exponential scale parameter. We propose fully sequential procedures and derive second order approximations to their average sample sizes and risks. Bias-corrected procedures are also proposed for both problems.

Keywords:

• Bounded risk
• Powers of scale parameter
• Fully sequential procedure
• Minimum risk problem
• Second order approximation
• Nonlinear renewal theory

Acknowledgments

The authors are very grateful to the referee for many constructive comments and suggestions which have led to an improved presentation of this work. The first author has been partially supported by a Grand-in-Aid for Science Research of the Ministry of Education, Science and Culture of Japan under contract numbers 11640106 and 14540107.

Recommended by M. Akahira