Shrinkage estimation of scale parameter of the extreme-value distribution

The author studies the usual preliminary test estimator of the scale parameter of the extreme-value distribution in censored samples. The optimum levels of significance and their corresponding critical values for the preliminary test are obtained based on the minimax regret criterion. A preliminary test shrinkage estimator that is smoother than the usual preliminary test estimator is proposed as well. The optimum values of shrinkage coefficients for the preliminary test shrinkage estimator are obtained, and are also based on the minimax regret criterion. Comparison of these two estimators shows that if the mean square error is a criterion of goodness of estimation then the preliminary test shrinkage estimator is better than the usual preliminary test estimator