Shrinkage Estimation of the Common Location Parameter of Several Exponentials

Abstract

Estimation of the common location parameter of several exponentials is considered. Using samples from m independent exponential populations with common location parameter θ, and given a prior guess θ₀ of θ, several shrinkage estimators have been proposed that incorporate this prior information. We propose shrinkage factors by minimizing the mean squared error or utilizing the P-values obtained from combining certain independent statistics and tests. A simulation study is conducted to investigate the performance of the proposed estimators. It is found that the proposed estimators are effective in taking advantage of the available prior information.

Key Words:

• Combination of independent tests
• Exponential distribution
• P-value
• Shrinkage estimation

Mathematics Subject Classifications:

• Primary 62F10
• Secondary 62P30

Acknowledgment

The author is grateful to the referee for his comments and suggestions that substantially improved the content and the style of the paper.