The Conditional Root Squares Estimation Of Regression Coefficient In Restricted Linear Regression Model

The restricted least square method is usually applied to estimate the regression coefficientβin restricted linear regression model.When multicollinearity of explanatory variables exact,Restricted least squares estimation loss its superior.Inspired by the idea of root squares,we present a new standard for estimating the regression coefficient of restricted linear regression model.Under the new standard we gain the estimation named conditional root squares estimation.In chapter 1,we discuss the existed theories and methods of linear model.In chapter 2,we give some pre-knowledge.In chapter 3 and 4,Based on the idea of root squares,we obtained the conditional root squares estimation(CRSE)and general the conditional root squares estimation(GCRSE)of regression coefficientβin restricted linear regression model,and discuss its biased,efficiency, admissibility.Because the conditional root squares estimation contains parametersκor K,we then discuss what the value ofκand K brings to the CRSE.Andκcan be chosen to make mean squares error(MSE)of the CRSE less than of the restricted least squares estimation(RLSE),we gain a necessary and sufficient condition which CRSE is superior to RLSE under the mean dispersion error(MDE)matrix comparisons criterion;and two of methods are used to evaluate the optimal value ofκ:Root Trace,Variance Inflation Factor.And K can be chosen to make MSE of the GCRSE less than of the CRSE,and gives display solution of generalize root squares estimator,proposes the methods of the optimal value ofκ.