Φ admissibility of linear estimators of common mean parameter in general multivariate linear models under a balanced loss function

Abstract

The definitions of $\Phi$ optimality and $\Phi$ admissibility of matrix common mean parameter are given in general multivariate linear models under a generalized matrix balanced loss function. We extend some previous studies to more general cases such that $\Phi$ admissibility of linear estimators on matrix common mean parameter. Sufficient and necessary conditions for linear estimators to be $\Phi$ admissible are obtained in classes of homogeneous and non homogeneous linear estimators, respectively.

Keywords:

• Multivariate linear models
• matrix common mean parameter
• balanced loss function
• linear estimators
• $\Phi$ admissibility

MSC 2000 SUBJECT CLASSIFICATIONS:

• 62C15
• 62J12

Additional information

Funding

Mingxiang Cao’s research is supported by the National Natural Science Foundation of China (Nos. 11601008, 11526070) and Doctor Startup Foundation of Anhui Normal University (No. 2016XJJ101). Guangjun Shen’s research is supported by the National Natural Science Foundation of China (No. 11271020) and the Distinguished Young Scholars Foundation of Anhui Province (No. 1608085J06).