Relationships between parameter estimations under a general linear model with explicit and implicit restrictions by rank of matrix

This thesis is organized in five parts. In the first chapter, an introduction is given by mentioning the purpose of the study. In the second part, some basic definitions and theorems and general information that will be required in our study are expressed. In the third section, the ordinary least squares estimators (OLSE) of several parametric functions under a general linear model and its explicit and implicit constrained models are considered. Furthermore, some relationships between these estimators and the ranks of model matrices in these models. In the fourth chapter, conclusions and recommendations are given. In the fifth chapter, the sources used in the thesis are listed.