An Application of Matrix Power Series to Linear Models

Abstract

In the system of two seemingly unrelated regressions, employing a matrix power series, we show that the two-stage estimator is better than the ordinary least square estimator (OLSE) in terms of the mean square error matrix (MSEM) criterion. The result enriches the existing literature and can be applied to many fields of applications related to economics and statistics.

Keywords:

• Matrix power series
• MSEM criterion
• Two-stage estimator

Mathematics Subject Classification:

• 62J05
• 62F10

Acknowledgments

The authors want to thank two careful referees and the Editor for very helpful comments and suggestions which led to this much improved version.

This article is partly supported by Scientific Foundation of BJTU (2007XM046) and NNSF of China (11171001).