Linearly admissible estimators on linear functions of regression coefficient under balanced loss function

Abstract

Linearly admissible estimators on linear functions of regression coefficient are studied in a singular linear model and balanced loss when the design matrix has not full column rank. The sufficient and necessary conditions for linear estimators to be admissible are obtained respectively in homogeneous and inhomogeneous classes.

Keywords:

• Linearly admissible estimator
• linear functions of regression coefficient
• singular linear model
• balanced loss function

2010 AMS SUBJECT CLASSIFICATIONS:

• Primary 62C15
• Secondary 62J05

Acknowledgements

We thank anonymous reviewers and the editor and the associate editor for helpful comments and suggestions. Dr. Cao’s research is supported by the National Natural Science Foundation of China (Nos. 11601008, 11526070), Anhui Provincial Natural Science Foundation (No. 1508085QA11), and Doctor Startup Foundation of Anhui Normal University (No. 2016XJJ101). Dr. He’s research is supported by the National Natural Science Foundation of China (No. 11201005).