On improved accelerated sequential estimation of the mean of an inverse Gaussian distribution

Abstract

This paper deals with developing an improved accelerated sequential procedure to estimate the unknown mean μ of an inverse Gaussian distribution, when the scale parameter λ also remains unknown. The problems of minimum risk and bounded risk point estimation are handled. Consideration is given to a weighted squared-error loss function. Our aim is to control the associated risk functions and obtain the second-order asymptotics as well. Further, we establish the superiority of this improved accelerated sequential sampling design over the Hall's accelerated sequential procedure in estimating an inverse Gaussian mean. Appropriate simulations and real data examples are also provided in support of the encouraging performance of our proposed methodology.

Keywords:

• Bounded risk
• improved accelerated sequential procedure
• inverse Gaussian distribution
• minimum risk
• risk per unit cost
• second-order asymptotics
• weighted squared-error loss

MATHEMATICS SUBJECT CLASSIFICATIONS::

• 62L12
• 62L05
• 62F12
• 62P30

Additional information

Funding

The authors are grateful to an associate editor and two anonymous reviewers for their constructive comments and suggestions on an earlier version, which greatly improved the presentation of this paper. Moreover, the first author, Neeraj Joshi is indebted to the Department of Science and Technology, Government of India for providing financial support for the research work under the INSPIRE fellowship program (Award No. - IF170889).