Mean squared error - a tool to evaluate the accuracy of parameter estimators in regression

Abstract

Linear regression model is frequently used to describe the relationship between a dependent variable and several independent variables. Thus, regression analysis is very useful in many application areas. In a linear regression model, there are unknown parameters to be estimated. The least squares estimator is most commonly used to estimate the unknown parameters. In addition, several other estimators are also proposed as alternatives to least squares estimator. A tool to evaluate the performance of these estimators is necessary. In this paper, mean squared error is shown as a tool to compare the accuracy of two estimators. An estimator with higher accuracy would be considered as a better estimator. As an example, two parameter estimators are compared using mean squared error as comparison tool. The parameter estimators are the Liu Estimator and the special case of Liu-type estimator