Permutation Matrix with Application to Optimal Invariant Quadratic Prediction in Finite Populations

Abstract

In this article, we primarily aim to apply the permutation matrix techniques to the problem of the optimal invariant quadratic prediction in a finite population. An alternative to the work of Liu and Rong (2007) is offered. In addition, we derive the OIQP for the population variance and show that it has less PMSE than the ordinary optimal unbiased predictor.

Keywords:

• Finite population
• Kronecker product
• OIQP
• Permutation matrix
• Population variance
• Symmetrizer matrix
• Vectorization

Mathematics Subject Classification:

• 15A09
• 15A06
• 60G25
• 62J05

Acknowledgments

The authors are grateful to the two anonymous referees and an Associate Editor for many valuable comments and suggestions which resulted in the present version. Thanks also to Professor N. Balakrishnan and Dr. Debbie Iscoe.

This research was supported by Grants HGQ0637 and HGQN0725 and the “Green & Blue Project” Program for 2008 to Cultivate Young Core Instructors from Huaiyin Institute of Technology.