Admissibility of linear estimators of the common mean parameter in general linear models under a balanced loss function

In order to investigate linearly admissible estimators of the common mean parameter in general linear models, we introduce and motivate the use of a balanced loss function obtained by combining Zellner’s idea of balanced loss (Zellner, 1994) with the unified theory of least squares (Rao, 1973). In c...

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Bibliographic Details
Published inJournal of multivariate analysis Vol. 153; pp. 246 - 254
Main Authors Cao, Ming-Xiang, He, Dao-Jiang
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2017
Subjects
Admissibility
Balanced loss function
Common mean parameter
Linear estimators
secondary
Balanced loss function
Admissibility
Linear estimators
Common mean parameter
primary
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Summary:In order to investigate linearly admissible estimators of the common mean parameter in general linear models, we introduce and motivate the use of a balanced loss function obtained by combining Zellner’s idea of balanced loss (Zellner, 1994) with the unified theory of least squares (Rao, 1973). In classes of homogeneous and non-homogeneous linear estimators, sufficient and necessary conditions for linear estimators of the common mean parameter to be admissible are obtained, respectively. A comparison is then made between linearly admissible estimators and a “truly” unified least square estimator.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2016.10.003