Second-order approximations for a multivariate analog of Behrens-Fisher problem through three-stage procedure

Abstract

In this article, we have proposed a three-stage procedure for the estimation of the difference of the means of two multivariate normal populations having unknown and unequal variances. Point as well as confidence region estimation is done for the same. Here, we have used the concept of classical Behrens-Fisher problem. Second-order approximations are obtained in both the cases, i.e., point estimation and confidence region estimation.

Keywords:

• Behrens-Fisher problem
• three-stage estimation
• second-order approximations
• point estimation
• confidence region estimation
• sequential sampling

MATHEMATICS SUBJECTS CLASSIFICATION:

• 62F10
• 62L12

Acknowledgements

The authors would like to sincerely thank the editor and the unknown referee for their valuable comments and suggestions. In particular, Neeraj Joshi is grateful to the Department of Science and Technology, Government of India for their financial support (INSPIRE fellowship IF170889, 2018) to pursue his research.