Pollution Of The Linear Regression Model Parameter Estimation

Linear model is one of the most important branches, which develops earlier and concludes more theories in mathematical statistics. During the past several hundred years, linear model is active in theory research which develops deeply. As a most popular part in the scientific research in the linear model, contaminated linear model attracts more eyes because of the widespread exist in actual life and has the very high value in the application.Contamination data is a common statistical data in Biological Statistics and Financial Statistics, it is also a incomplete data. However, the use of incomplete data is not entirely. Although sometimes we can do a statistical data, but most of the time it is cannot be duplicated, time-consuming too long or the price too is high. Moreover, in the situation which the stationary source has not verified or eliminated, we only obtain the contaminated data. This paper importantly studies the estimation of parameter in linear regression model which contains contamination data.The first chapter introduces the background of this topic, as well as domestic and foreign research and some preparatory knowledgement.In the second chapter the single linear regression model of contamination data is promoted to the multi-dimensional linear regression model, we estimate the regression coefficient and contamination coefficient by least squares estimation, and prove the strong consistency of estimations of regression coefficient and contamination coefficient. We also give the interval estimation of parameters on the condition that the error distribution is normal.In the third chapter we obtain the parameter estimation with the restrict of linear, meanwhile , we prove that the strong consistency of these estimation.The forth chapter displays the estimation of coefficients with the principle of universal least squares estimation when the design matrix is ill-conditioned or rank-defieient.We put forwardα₀ class of universal least squares estimation on the basisof improvement on estimation .In the end, we get the estimation of regression and contamination coefficient by using the method ofα₀ class of universal least squaresestimation.