A matrix approach to a general partitioned linear model with partial parameter restrictions

ABSTRACT

This article considers some fundamental estimation problems on a general partitioned linear model with partial parameter restrictions. We shall derive analytical formulas for calculating the ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) of the whole and partial parameter vectors in the model and its reduced models, and establish identifying conditions for the equivalence of the OLSEs and BLUEs under among these models.

KEYWORDS:

• Partitioned linear model
• reduced model
• estimability
• OLSE
• BLUE
• generalized inverse
• rank formula

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 15A09
• 62H12
• 62J05

Acknowledgments

The authors are grateful to an anonymous referee for helpful comments and suggestions on an earlier draft of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.