Parameter estimations under partitioned linear models and some relations between parameter estimators

This thesis is organized in six parts. In the first chapter, an introduction is given by mentioning the purpose of the study. In the second chapter, the basic definitions, theorems and general information that will be required in our study are expressed. In the third chapter, the ordinary least squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of parameters under a general linear model and its equality constrained model are considered. Also, some necessary and sufficient conditions are investigated for equalities of estimators under a general linear model and its constrained model. In the fourth chapter, the ordinary least squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of parameters under partitioned linear model are considered. Furthermore, some necessary and sufficient conditions are investigated for equalities of estimators under equality or inequality constrained partitioned linear models. In the fifth chapter, conclusions and recommendations are given. In the sixth chapter, the sources used in the thesis are listed.