Improved estimation of a function of scale parameter of a doubly censored exponential distribution

Abstract

In the present article, we have studied the estimation of the reciprocal of scale parameter $1/\sigma$, that is, hazard rate of a two parameter exponential distribution based on a doubly censored sample. This estimation problem has been investigated under a general class of bowl-shaped scale invariant loss functions. It is established that the best affine equivariant estimator (BAEE) is inadmissible by deriving an improved estimator. This estimator is non-smooth. Further, we have obtained a smooth improved estimator. A class of scale equivariant estimator is considered and sufficient conditions are derived under which these estimators improve upon the BAEE. In particular, using these results we have obtained the improved estimators for three special loss functions. A simulation study is conducted to compare the risk performance of the proposed estimators. Finally, we analyze a real data set.

Keywords:

• Decision theory
• best affine equivariant estimator
• brewster and Zidek-type estimators
• doubly censored sample
• scale invariant loss function

Acknowledgments

This article was partially completed while author, B. M. Golam Kibria was on sabbatical leave (Fall 2017). He is grateful to Florida International University for awarding the sabbatical leave which gave him excellent research facilities. The authors thank the reviewers for their valuable suggestions which have considerably improved the content and the presentation of the article.