Predictions and estimations under a group of linear models with random coefficients

ABSTRACT

This article investigates the problem of establishing best linear unbiased predictors and best linear unbiased estimators of all unknown parameters in a group of linear models with random coefficients and correlated covariance matrix. We shall derive a variety of fundamental statistical properties of the predictors and estimators by using some matrix analysis tools. In particular, we shall establish necessary and sufficient conditions for the predictors and estimators to be equivalent under single and combined equations in the group of models by using the method of matrix equations, matrix rank formulas, and partitioned matrix calculations.

KEYWORDS:

• BLUE
• BLUP
• Decomposition
• Equality
• Linear model
• Random coefficients

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H12
• 62J05

Acknowledgments

The authors thank an anonymous referee for his/her helpful comments and suggestions on an earlier version of this article.