SHRINKAGE PREDICTION IN THE EXPONENTIAL DISTRIBUTION WITH A PRIOR INTERVAL FOR THE SCALE PARAMETER

Abstract

The author proposes the best shrinkage predictor of a preassigned dominance level for a future order statistic of an exponential distribution, assuming a prior estimate of the scale parameter is distributed over an interval according to an arbitrary distribution with known mean. Based on a Type II censored sample from this distribution, we predict the future order statistic in another independent sample from the same distribution. The predictor is constructed by incorporating a preliminary confidence interval for the scale parameter and a class of shrinkage predictors constructed here. It improves considerably classical predictors for all values of the scale parameter within its dominance interval containing the confidence interval of a preassigned level.

Keywords:

• Shrinkage predictor
• Preliminary confidence interval
• Dominance interval
• Dominance level
• Best linear invariant predictor
• Two-sample prediction problem
• Relative improvement

ACKNOWLEDGMENTS

The author would like to thank the referees for their helpful comments and suggestions. Thanks are also due to Associate Professor Takeshi Ishikawa, Shonan Institute of Technology, Former Associate Professor Kyo Miyakawa and Associate Professor Takanori Tamiya, Science University of Tokyo, for their helpful comments and encouragements. Especially the author expresses gratitude to Tadashi Ikuta, a graduate student of Science University of Tokyo, for having drawn figures.