Recently, much attention has been paid to the criterion comparison of parameter estimators, which was introduced in 1937 by Pitman. The new research results show that from both theoretical and practical points of view there are some reasons for giving preference of the Pitman criterion over the mean square error. However, the Pitman criterion has two main weaknesses: the complexity of computation and the intransitivity. “’” Recently, much attention has been paid to the criterion comparing of parameter estimators, which was introduced in 1937 by Pitman. The new research results show from from both theoretical and practical points of view there are some reasons for giving preference of the Pitman criterion over the However, the Pitman criterion has two main weaknesses: the complexity of computation and the intransitivity. “’”