Parameter Estimation And Comparison Of Linear Regression Model Under Partial Normal Error Distribution

This essay mainly studied the parameter estimation problem of the one-dimensional linear regression under partial normal error distribution N(0, ?2). However, the error term does not necessarily obey the normality assumption in many fields of the application of the linear model. Therefore, the normality hypothesis under the linear regression model is extended to the Skewed Normal Distribution in this paper. That is, under the assump-tion of partial normal distribution, the estimation method of the target parameters in the regression model is discussed.This paper is divided into four parts; The first part includes the background informa-tion of this problem, origins of the problem, the current research findings, and the relative methods used in this paper. In the second part, based on subdivision and the Maximum Likelihood Estimation method, the model-based parameter estimation has been solved after improving. The third is to solve the parameter estimation of the model under the principle of Moment Estimation, Least Absolute Deviation Estimation and Least Squares Estimation. In the fourth part, the numerical simulation of the above-mentioned various estimation methods is carried out. By calculating the mean square error and the relative error of the target parameters, The accuracy and stability of the judge of each estimation method are given.