@article{Ren2025, 
author = {Xingwei Ren},
title = {Statistical inference of the mixed linear model with incorrect stochastic linear restrictions},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {5},
pages = {11349-11368},
keywords = {mixed linear model, correct stochastic restrictions, incorrect stochastic restrictions, matrix rank, BLUP},
url = {https://www.sciopen.com/article/10.3934/math.2025516},
doi = {10.3934/math.2025516},
abstract = {We considered the general mixed linear model        N   subject to two competing stochastic linear restrictions,              M              0       and        M  , where the restrictions        M   are the correct information whereas restrictions              M              0       may be incorrect. Statistical inference conclusions of using the above two competing restrictions are not necessarily the same, so it is prominent to discuss the relationships between incorrect restrictions              M              0       and the corresponding correct restrictions        M   in the context of model        N  . In this article, we first present some properties on the best linear unbiased predictors (BLUPs) under model        N   with restrictions        M  . We then provide necessary and sufficient conditions under which the BLUPs under        N   with the incorrect restrictions              M              0       continue to be BLUPs associated with correct restrictions.}
}