Hamid Karamikabir

Today, regression is widely used for prediction in the topic of machine learning. In the analysis of regression problems, especially in the statistical modelling of economic data, psychology, social sciences, vital, engineering, etc., in some cases we face the problem of collinearity among independent variables and correlation in errors. One of the types of regression that is of interest due to its simplicity is linear regression. In this thesis, some types of linear regression will be investigated. For this purpose, we refer to the introduction of compensated regression types to solve the collinearity problem. In this regard, we have investigated the stighi and lasso regressions, and in the following, we are trying to solve the collinearity problem by introducing the stochastic bounded stighi regression. In particular, in this thesis, the contraction and mixed regression estimators as well as the generalized least squares estimator are introduced. At the end, the correlation between errors is checked for real data, and it is also shown that the stochastic bounded regression estimator has less variance and more efficiency than the contraction and mixed estimator.