Biased Estimation Of Regression Coefficient In Restricted Linear Regression Model With Missing Data

The research of the biased estimation of parameters in the linear model is all the time one of the most popular issues of regression analysis.While dealing with the multicollinearity of design matrix X,the ordinary least squares estimation is always helpless.The linear biased estimation is the most direct method in ameliorating the ordinary least squares estimation.The development of the biased estimation theory of parameters has been relatively mature in the linear regression model without additional restrictions.In a great deal of statistical problems such as in the experiment design,the models of the variance analysis and the covariance analysis and so on,because of additional information and other reasons,regression parameters meet certain restrictive conditions, which show in practice the investigative significances and the applied values of the restricted linear regression.Like the ordinary least squares estimation,the widely applied ordinary restricted least squares estimation is also disadvantageous for dealing with the multicollinearity of design matrix.As a result,a great many researchers recently try to find out better methods to improve the ordinary restricted least squares estimation.In this dissertation,wetry to seek some biased estimations better than the ordinary restricted least squares estimation in restricted linear regression model.Besides,present a new standard(MDE) for estimating the regression coefficient of restricted linear regression model,and give a new restricted biased estimation of regression coefficient——conditional partial root squares estimation and it is introduced into restricted linear regression model with missing data,and investigate the features of the restricted ridge estimation of regression coefficient in model(4.2) with missing data.In chapter 1,we discuss the history of development and the current situation of the biased estimation in the linear regression model.In chapter 2,we give some pre-knowledge.In chapter 3,on the basis of Guo Jian-Feng and Shi Jian-hong,the author give a new permissible estimation——Conditional partial root squares estimation(CPRSE),prove the existence of parameters k of making mean squares error(MSE) of the Conditional partial root squares estimation less than that of the restricted least squares estimation(RLSE). We gain a necessary and sufficient condition or sufficient conditions which CPRSE is superior to RLSE under the mean dispersion error(MDE) matrix comparisons criterion;and some of methods are discussed to evaluate the optimal value of k.In chapter 4,we research the restricted linear regression model with missing data and imputation methods in missing data,and we have access to conditional partial root squares estimation(CPRSE) of regression coefficient in restricted Linear regression model with missing data.In chapter 5,we give the restricted ridge estimation of regression coefficientβin model(4.2) with missing data and k can be chosen to make mean squares error(MSE) of the restricted ridge estimation(RRE) less than of the restricted least squares estimation(RLSE),we gain a necessary and sufficient condition or sufficient conditions which' RRE is superior to RLSE under the mean dispersion error(MDE) matrix comparisons criterion.