Some Matrix Norm Kantorovich Inequalities and Their Applications

Abstract

In this article, we first present four matrix norm Kantorovich-type inequalities involving non negative definite matrix. Then, based on these inequalities, we propose four new efficiency criteria and present their lower bounds to make efficiency comparisons between the ordinary least squares estimator and the best linear unbiased estimator in a singular linear model.

Keywords:

• Best linear unbiased estimator
• Kantorovich inequality
• Matrix norm inequalities
• Ordinary least squares estimator

Mathematics Subject Classification:

• 15A45
• 15A60
• 62J05

Acknowledgments

The authors are most grateful to the anonymous reviewer and the editor for valuable comments and suggestions which helped to improve the quality of the presentation. The work was supported by the Fundamental Research Funds for the Central Universities (No. CDJZR10100002).