Best Quadratic Unbiased Prediction in a General Linear Model with Stochastic Regression Coefficients

Abstract

In this article, we discuss on how to predict a combined quadratic parametric function of the form β′ H β + hσ² in a general linear model with stochastic regression coefficients denoted by y  =  X β +  e . Firstly, the quadratic predictability of β′ H β + hσ² is investigated to obtain a quadratic unbiased predictor (QUP) via a general method of structuring an unbiased estimator. This QUP is also optimal in some situations and therefore we hope it will be a fine predictor. To show this idea, we apply the Lagrange multipliers method to this problem and finally reach the expected conclusion through permutation matrix techniques.

Keywords:

• Best quadratic unbiased predictor
• Permutation matrix
• Quadratic predictability
• Stochastic regression coefficient

Mathematics Subject Classification:

• 60G25
• 62J05
• 15A09

Acknowledgments

The authors are grateful to the anonymous referee for the his/her careful reading and constructive criticisms which have improved the article substantially in the final version. Great thanks are also given to Prof. Jing-Guang Li (Huaiyin Institute of Technology) for his beneficial suggestions in the whole process of revising this article.

This research was supported by Grants HAS08036 and HGC0923 and the “Green & Blue Project” Program for 2008 for Cultivating Young Core Instructors from Huaiyin Institute of Technology.