Analysis of Optimal Prediction Under Stochastically Restricted Linear Model and Its Subsample Models

This paper provides a study on optimal prediction problems in a linear model and its subsample models with linear stochastic restrictions, using matrix theory for precise analytical solutions. It focuses on deriving analytical expressions using block matrix inertia and rank methods to determine which of the best linear unbiased predictors (BLUPs) of a general vector of unknown parameters is superior to others under a stochastically restricted linear model and its subsample models. Additionally, this study examines the comparative results of the best linear unbiased estimators of unknown parameters. The comparisons in the study are based on the mean squared error matrix (MSEM) criterion. Finally, a numerical example is given to illustrate the theoretical results.