Abstract
Estimation and prediction of regression models with partition forms are widely applied techniques in statistical inference and data analysis. In this paper, we consider some fundamental inference problems regarding a linear random-effects model (LREM) and its reduced models without statistical distribution assumptions for error terms. We shall present a partition form of LREM and its correctly-reduced models, introduce the consistency concepts of the LREM and its reduced models, define the predictability/estimability of unknown parameters in the LREM and its reduced models, establish the matrix equations and analytical formulas associated with best linear unbiased predictors (BLUPs) and best linear unbiased estimators (BLUEs) of all unknown parameter vectors in the LREM and its reduced models, and present many fundamental decomposition equalities for the BLUPs/BLUEs of all unknown parameters in the LREM and its reduced models.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
