Abstract
Estimations of unknown parameters in linear regression models have been main objects of study in statistical data analysis and inference. This work concerns the comparison problem of different estimations of unknown parameters in two linear random-effects models (LREMs) with different structures. We shall derive analytical formulas for calculating best linear unbiased predictors/best linear unbiased estimators (BLUPs/BLUEs) of all unknown parameter spaces in the two competing LREMs. We then discuss relationships among BLUPs/BLUEs under the two LREMs by using some matrix analysis tools, including various consequences and conclusions on some special cases of LREMs.
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