A preliminary test procedure for the scale parameter of exponential distribution when the selection parameter is unknown

Summary A preliminary test estimator is considered for the scale parameter of the two-parameter exponential distribution with unknown selection parameter, where the distribution does not satisfy the regularity condition of Wilks' theorem—the density is not differentiable. A method of specifying the level of significance of the preliminary test based on is proposed AIC. This work was partly supported by Scientific Research Fund No. 58450058 from the Ministry of Education of Japan. The Institute of Statistical Mathematics