On a Biased Prediction Based on Optimal Mean Square Error Criterion

Given a linear statistical model, statisticians have established many kinds of optimality criteria for estimating/predicting unknown parameters in the model using various mean square error methods. In this work, we revisit the well-known mean square error matrix (MSEM) for estimating/predicting unknown parameters in the context of general linear models from a completely new perspective. The coverage includes giving the definitions and analytical expressions of the minimum mean square error matrix predictor (MMSEMP) of a joint vector of all unknown parameters in the linear model by solving a quadratic matrix value optimization problem, and discussing a diverse of algebraic and statistical properties and additive decomposition equality of these predictors using some precise matrix analysis tools.