Estimating powers of the scale parameters under order restriction for two shifted exponential populations with a common location

Abstract

This article investigates the problem of estimating the powers of scale parameters under order restriction of two shifted exponential populations when the location parameters are assumed to be unknown and equal. Several classical estimators have been proposed, such as the maximum likelihood estimators, plug-in type restricted maximum likelihood estimators, and the uniform minimum variance unbiased estimators. Sufficient conditions for constructing improved estimators under the scale and affine group of transformations have been derived. Consequently, several improved estimators for the powers of the scale parameters under order restriction have been proposed. Furthermore, using the quadratic loss function, a simulation study has been carried out to compare all the proposed estimators in terms of risk values, and recommendations are made there.

Keywords:

• Equivariant estimators
• improved estimators
• inadmissibility
• order restriction
• powers of scale parameters
• simulation study

AMS Subject Classification 2010:

• 62C15
• 62F10
• 62F30

Acknowledgment

The authors would like to sincerely thank the two anonymous reviewers and the associate editor, whose constructive and thoughtful comments on the earlier version of the manuscript led to greater improvements of manuscript’s content.

Disclosure Statement

The authors have no competing interests to declare that are relevant to the content of this article.