Inertia and rank approach in transformed linear mixed models for comparison of BLUPs

Comparison of BLUPs under multiple partitioned linear model and its correctly-reduced models

“…For more details on inertias and ranks of symmetric matrices and relations between inertias and L öwner partial ordering of symmetric matrices, see, e.g., [15,18,19,24]. As further reference for comparison of covariance matrix of predictors/estimators by using matrix rank/inertia method, we may mention [6,22,23] among others. More related work on prediction/estimation problems under partitioned linear models can be found in; see, e.g., [5, 7-12, 14, 17, 25].…”

“…Characterization of fundamental BLUP properties can be found in the statistical literature. The similar approach used in proof of Theorem 1 given below was used for transformed linear mixed models in [6], for the different approaches; see, e.g., [15,21].…”

On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models

“…The fundamental results on BLUP of φ 1 under (1.6) and (1.7) are collected in the following theorems. The results given below are obtained from [24] by considering the models and notation used in this paper. For different approaches; see, e.g, [23], [25].…”