Linear estimators under Pitman nearness criterion
Recently, much attention has been paid to the comparison criterion of parameter estimators introduced by \textit{E. J. Pitman} [Proc. Cambridge Philos. Soc. 33, 212-222 (1937; Zbl 0016.36404)]. New research results show that from both theoretical and practical points of view there are some reasons for giving preference to the Pitman criterion over the mean square error criterion. However, the Pitman criterion has two main weaknesses: the complexity of computation and the intransitivity. \textit{R. L. Mason} et al. [J. Am. Stat. Assoc. 85, No. 410, 579-581 (1990; Zbl 0702.62049)] and \textit{S. D. Peddada} et al. [Commun. Stat., Theory Methods 20, No. 11, 3525-3534 (1991)] studied the comparison of two linear estimators using the Pitman criterion and provided some sufficient conditions for preference of 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 set on which a linear estimator is superior to another linear estimator. The results obtained here are further developments and improvements of Mason et al. and Peddada et al.
scientific article; zbMATH DE number 854898