Estimation of order restricted standard deviations of normal populations with a common mean

Abstract

The present paper deals with estimating standard deviations of two normal populations with a common mean and ordered variances. We propose a class of improved estimators of the standard deviations under the quadratic loss function. Considering k normal populations with a common mean and ordered variances, we establish inadmissibility results of the affine and scale equivariant estimators of the smallest standard deviation and derive its improved estimators. Simulation studies are performed to compare the risks of the improved estimators with the existing estimators. Two illustrative examples are presented as applications of the proposed estimators.

Keywords:

• Unbiased estimator
• affine equivariant estimator
• scale equivariant estimator
• smallest standard deviation
• Brewster-Zidek technique
• Monte-Carlo simulation

Mathematics Subject Classifications:

• 62F30
• 62F10

Acknowledgments

The authors would like to thank two reviewers, associate editor and editor for their valuable comments and suggestions which led to the substantial improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research work of the first author is supported by a grant from the Science and Engineering Research Board, Govt. of India (Grant No. ECR/2017/000255).