Multi-Stage Estimation Methodologies for an Inverse Gaussian Mean with Known Coefficient of Variation

Abstract

In this paper, we develop accelerated sequential and $k-$stage $(k\ge 3)$ procedures for estimating the mean of an inverse Gaussian distribution when the population coefficient of variation is known. The problems of minimum risk and bounded risk point estimation are handled. The estimation procedures are developed under an interesting weighted squared-error loss function and our aim is to control the associated risk functions. In spite of the usual estimator, i.e., the sample mean, Searls (1964) estimator is utilized for the purpose of estimation. Second-order asymptotics are obtained for the expected sample size and risk associated with the proposed multi-stage procedures. Further, it is established that the Searls’ estimator dominates the usual estimator (sample mean) under the proposed procedures. Extensive simulation analysis is carried out in support of the encouraging performances of the proposed methodologies and a real data example is also provided for illustrative purposes.

Keywords and Phrases:

• Accelerated sequential
• bird surveys data
• bounded risk
• coefficient of variation
• inverse Gaussian distribution
• $\mathit{k}-$stage procedure
• minimum risk
• point estimation
• Searls’ estimator
• second-order asymptotics
• weighted squared-error loss

Mathematics Subject Classifications:

• 62L05
• 62L10
• 62L12
• 62F10
• 62F12

Acknowledgments

The authors are indebted to the Editor and the anonymous referee(s) 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 grateful to “Late Professor Ajit Chaturvedi” for all the fruitful discussions on the present research problem.

Additional information

Funding

Neeraj Joshi is also 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).