Estimating a linear parametric function of a doubly censored exponential distribution

ABSTRACT

For an arbitrary strictly convex loss function, we study the problem of estimating a linear parametric function $\mu +k\sigma ,k$ is a known constant, when a doubly censored sample is available from a two-parameter exponential $E(\mu ,\sigma )$ population. We establish the inadmissibility of the best affine equivariant (BAE) estimator by deriving an improved estimator. We provide various implications for quadratic and linex loss functions in detail. Improvements are obtained for the absolute value loss function as well. Further a new class of estimators improving upon the BAE estimator is derived using the Kubokawa method. This class is shown to include some benchmark estimators from the literature.

KEYWORDS:

• Brewster-Zidek estimator
• censored samples
• inadmissibility
• equivariant estimator

MSC 2010:

• 62C99
• 62F10

Disclosure statement

No potential conflict of interest was reported by the authors.

Acknowledgments

We are grateful to a referee for his encouragement and constructive suggestions that led to significant improvements in the presentation and contents of this paper. Authors also extend their sincere thanks to the Editor for his helpful comments.

ORCID

C. Petropoulos http://orcid.org/0000-0001-5185-7037

Additional information

Funding

The authors Yogesh Mani Tripathi and Farha Sultana gratefully acknowledge the financial support for this research work under a grant SR/S4/MS:785/12 from the SERB, Department of Science & Technology, India