Linear estimators under Pitman nearness criterion
type: Item
instance of: scholarly article
title: Linear estimators under Pitman nearness criterion
zbMATH Open document ID: 0851.62037
author: Hu Yang
author: Songgui Wang
published in: Chinese Science Bulletin
publication date: 1996-11-11T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 854898
zbMATH Keywords: loss function
zbMATH Keywords: nearness measure
zbMATH Keywords: mean square error
zbMATH Keywords: linear estimators
zbMATH Keywords: Pitman criterion
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 854898