Linear estimators under Pitman nearness criterion

摘要

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 givingpreference of the Pitman criterion over the mean square error. However, the Pitman criterion has two main weaknesses: the complexity of computation and the intransitivity. Mason et al. and Peddada et a/. studied the comparison of two linear estimators using Pitman criterion and provided some sufficient conditions for preference pf an estimator over another. In fact, however, there are only rare cases in which their conditions are satisfied. The purpose of this note is to characterize the parameter seton which a linear estimator is superior to another linear eatimator. The results obtained here are the further development and inprovement of references [7, 8].