Space Decomposition and Estimation in Multivariate Linear Models

Linear models are important in statistical analysis. In many real situations, these models become more and more complex, as such the estimation of model parameters constitutes a big challenge. To overcome this challenge many approaches have been proposed and space decomposition has emerged as a powerful tool in handling these complex models. This work gives a comprehensive review of some of challenges related to complex multivariate models and how the space decomposition has been successfully used. In this review, we first present the space decomposition as a tool to decompose complex models into tractable models that are easy to handle for estimation and testing. On the other hand, we give another space decomposition approach used for obtaining explicit estimators in multivariate linear models. Some examples on how this decomposition is performed for specific multivariate linear models are presented for both approaches.