Study On Estimation Of Parameters And Its Relative Efficiency In Linear Regression Model With Restrictions

Linear model is a mathematical model,which uses linearity to describe the relationship between independent variable and dependent variable.Because of its simple form,it has become widely used in modern statistics.Based on the linear regression model with restrictions,this paper discusses parameter estimation and its relative efficiency mainly.(1)Weighted mixed estimate is very important in the theory of parameter estimation of linear regression model with constraint conditions,but it includes unknown matrix.We usually replace it by least square estimate in practical application.So this paper discusses the problem of relative efficiency of the weighted mixed estimate with respect to least squares estimate.First,we give four kinds of new relative efficiency.Then,the lower and upp er bound of three kinds of relative efficiency and the relation among different relative efficiency are obtained.Last,we use a numerical example to illustrate our theoretical results.(2)Least squares estimate plays a fundamental role in the parameter estimation theory.However,it is not ideal in the theoretical analysis when the design matrix is multi-colinearity.So this paper continues to discuss the problem of parameter estimation.First,we propose a new estimate called almost unbiased weighted mixed two-parameter estimate by unifying almost unbiased two-parameter estimate with the weighted mixed estimate.Then,in the mean squared error matrix sense,we derive the necessary and sufficient conditions for the superiority of the new estimator over t he almost unbiased two-parameter estimate,O LS,almost unbiased weighted mixed ridge estimate.Furthermore,we obtain the optimal values of k,d.Last,we discuss the relative efficiency of new estimate with least squares estimate.We give two kinds of relative efficiency and obtain the lower and upper bounds of relative efficiency.