General ridge predictors in a mixed linear model |
| |
Authors: | Xu-Qing Liu Ping Hu |
| |
Affiliation: | 1. Faculty of Mathematics and Physics , Huaiyin Institute of Technology , Huai'an , 223003 , People's Republic of China liuxuqing688@gmail.com;3. Faculty of Mathematics and Physics , Huaiyin Institute of Technology , Huai'an , 223003 , People's Republic of China |
| |
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 |
|
|