Preliminary Test Estimation of the Threshold in the Two-Parameter Exponential Distribution Based on Records and Minimax Regret Significance Levels

SYNOPTIC ABSRACT

We consider preliminary test estimation of the threshold parameter of the two-parameter exponential distribution using record-breaking data. We use the minimax regret criterion on the risk function of the preliminary test estimator to obtain the optimal significance levels for the preliminary test. The optimal levels and the corresponding critical values are numerically obtained. An illustrative example is given.

KEY WORDS AND PHRASES:

• Maximum likelihood estimator
• minimax regret criterion
• preliminarytest estimator
• exponential distribution
• threshold parameter

Acknowledgments

The author would like to thank the anonymous reviewer for their careful reading of the article, and for their extensive comments and suggestions that resulted in a much-improved version.