Characterization of Admissible Linear Estimators in Multivariate Linear Model with Respect to Inequality Constraints under Matrix Loss Function

Abstract

In this article, we study the characterization of admissible linear estimators in a multivariate linear model with inequality constraint, under a matrix loss function. In the homogeneous class, we present several equivalent, necessary and sufficient conditions for a linear estimator of estimable functions to be admissible. In the inhomogeneous class, we find that the necessary and sufficient conditions depend on the rank of the matrix in the constraint. When the rank is greater than one, the necessary and sufficient conditions are obtained. When the rank is equal to one, we have necessary conditions and sufficient conditions separately. We also obtain the necessary and sufficient conditions for a linear estimator of inestimable function to be admissible in both classes.

Keywords:

• Admissibility
• Homogeneous/Inhomogeneous linear estimation
• Inequality constraints
• Matrix loss
• Multivariate linear model

Mathematics Subject Classification:

• 62C05
• 62F10

Acknowledgment

We are grateful for many valuable discussions with Professor Lynn A. LaMotte. We also thank the Editor, Professor N. Balakrishnan, and anonymous reviewers for their constructive comments. Zhang's research was supported by National Science Foundation of China (61070236, 60736047) and the Project of State Key Laboratory of Rail Traffic Control and Safety (No: RCS2010K005), Beijing Jiaotong University.