Several Properties Of Maximum Likelihood Estimation In Linear Regression Models

In the historical tide of statistical development,regression model is a kind of statistical model which has been put forward earlier,and the theoretical knowledge is perfect,and the application performance has its unique charm also because of the need to solve practical problems,the regression model has been in the process of continuous development and progress.and the linear model is also a statistical object that applied the concept of statistics earlier.it includes linear regression model,analysis of variance model,covariance model,experimental design model,random mixed effect model,generalized linear model(GLM).Therefore,the basic and important linear regression model should be taken as the starting point to study the statistical problems.One statistical model for determining the quantitative relationship between two or more variables is very extensive,and in the study of such problems parameter estimation is a focus problem,which is the basis of other statistical problems.At present,the most widely used method of parameter estimation in linear regression model is Maximum likelihood estimation method(maximum likelihood estimation MLE),which is based on the principle of maximum likelihood,and the MLE obtained are of good properties,such as measurability,invariance,existence,soleability.homogeneity,compatibility,progressive normality,effectiveness,robustness and asymptotic robustness,etc,in a sense,there is no better parameter estimation than MLE,and it is also widely used in various fields of society.In this paper,the existence and correlation of maximum likelihood estimation in truncated linear regression model are studied,and the consistency and progressiveness of the root of likelihood equation in Cauchy distribution family are studied,and verified by examples.