Parameter estimation under constrained multivariate linear model

In statistical analysis, linear models occupy a significant place. Particularly in multivariate linear models, parameter estimation and interpretations have a wide range of applications in the literature. Studies in this area often focus on explaining a single dependent variable with a group of explanatory variables. However, in real-world scenarios, problems involving two or more dependent variables simultaneously are frequently encountered. Such situations demonstrate the need for more general structures that go beyond classical multivariate models. This thesis focuses on constrained multivariate linear models and their over-parameterized version. The aim is to derive analytical formulas for the Best Linear Unbiased Predictor (BLUP) and the Best Linear Unbiased Estimator (BLUE) of all unknown parameter matrices under these models. However, the constraints on the unknown parameter matrix complicate the process within the framework of the given models. In the study, the constraints are eliminated using the reparameterization method to overcome this difficulty. Thus, for the new models obtained, analytical formulas for BLUP/BLUE of all unknown parameter matrices are derived using quadratic matrix optimization techniques. As a result, new and valuable features are gained for BLUP/BLUE.