Estimation of the location parameter and the average worth of the selected subset of two parameter exponential populations under LINEX loss function

ABSTRACT

Suppose a subset of populations is selected from k exponential populations with unknown location parameters θ₁, θ₂, …, θ_k and common known scale parameter σ. We consider the estimation of the location parameter of the selected population and the average worth of the selected subset under an asymmetric LINEX loss function. We show that the natural estimator of these parameters is biased and find the uniformly minimum risk-unbiased (UMRU) estimator of these parameters. In the case of k = 2, we find the minimax estimator of the location parameter of the smallest selected population. Furthermore, we compare numerically the risk of UMRU, minimax, and the natural estimators.

KEYWORDS:

• Estimation after selection
• LINEX loss function
• Minimax estimation
• Two-parameter exponential distribution
• Uniformly minimum risk-unbiased estimator.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62F07
• Secondary 62F10, 62C20

Acknowledgments

The authors are grateful to the editor and an anonymous referee for making helpful comments and suggestions on an earlier version of this article.