General ridge predictors in a mixed linear model

Abstract

This paper mainly aims to put forward two estimators for the linear combination of fixed effects and random effects, and to investigate their properties in a general mixed linear model. First, we define the notion of a Type-I general ridge predictor (GRP) and obtain two sufficient conditions for a Type-I GRP to be superior over the best linear unbiased predictor (BLUP). Second, we establish the relationship between a Type-I GRP and linear admissibility, which results in the notion of Type-II GRP. We show that a linear predictor is linearly admissible if and only if it is a Type-II GRP. The superiority of a Type-II GRP over the BLUP is also obtained. Third, the problem of confidence ellipsoids based on the BLUP and Type-II GRP is investigated.

Keywords:

• general mixed linear model
• best linear unbiased predictor
• BLUP
• general ridge predictor
• GRP
• linear admissibility
• confidence ellipsoid
• ellipsoidal restriction
• linear restriction

MSC 2000 :

• 62C15
• 62F10
• 62H12

Acknowledgements

The authors are grateful to the referees for valuable comments and constructive suggestions which resulted in the present version. Our sincere thanks to Professor Jing-Guang Li for helpful suggestions. The research was supported by Grants HGC0923 and HGC0925 from Huaiyin Institute of Technology. The first author is sponsored by the Qing Lan Project from the Jiangsu province.