A class of general pretest estimators for the univariate normal mean

In this paper, we propose a class of general pretest estimators for the univariate normal mean. The main mathematical idea proposed is adaptation randomized tests, where randomization probability related to shrinkage parameter. Consequently, includes many existing estimators, such as pretest, shrinkage, Bayes, and empirical Bayes special cases. Furthermore, can be easily tuned users by adjusting significance levels function. We derive theoretical properties class, expressions distribution function, bias, MSE. Our bias MSE turn out simpler than those previously derived some formulas also conduct simulation studies examine our results demonstrate application through real dataset.