The weighted hybrid estimation for linear mixed models with measurement error under stochastic linear mixed restrictions

In this article, we propose a new hybrid estimator and predictor for fixed and random effects in linear mixed models with measurement error, particularly in the presence of multicollinearity. Furthermore, a weighted stochastic restricted hybrid estimator and predictor is developed by incorporating additional stochastic linear restrictions on both fixed and random effects. The asymptotic properties of the proposed estimators are investigated, and their performance is evaluated and compared with existing methods using the mean squared error matrix (MSEM) criterion. A comprehensive Monte Carlo simulation study and a real data analysis are conducted to demonstrate the effectiveness and superiority of the proposed approach.