Research On The Method Of Biased Estimation With Stochastic Restriction In Linear Model

For a long time,parameter estimation is a very important research content in linear model.The most commonly used parameter estimation method is the least square estimation method.However,when multicollinearity is found to exist widely,the least square estimation method is no longer advantageous.In view of the shortcomings of the least square method in dealing with multicollinearity,many scholars have proposed various biased estimates.Among them,the most important ones include ridge estimation,principal component estimation,Liu estimation and two parameter estimation.At the same time,some scholars consider that adding restrictions to the parameters of linear model can also deal with multicollinearity problems,such as restricted least square estimation and hybrid estimation.Based on the previous research,this paper combines the constraints with prior information and biased estimation methods,and makes further discussion and research on parameter estimation to further solve the multicollinearity problem and improve the estimation effect of model parameters.The main work and achievements are as follows:1.For the linear model with stochastic constraints,the paper first transforms the mixed estimation form,and then proposes an improved stochastic restricted Liu estimation combining the Liu type estimation.We prove that the property of the new estimation is excellent and benign,and verify that the improved estimation has better parameter estimation effect through the actual data and Monte Carlo simulation.Then a new stochastic restricted Liu type estimator is proposed by combining another new Liu type estimator and hybrid estimator.When the constraint condition is true or not,the necessary and sufficient condition conditions are proved to be better than the new Liu type estimator and hybrid estimator.Finally,the new estimator is proved to have better parameter estimation effect by case analysis.2.Then,a new stochastic restricted two parameter estimation is proposed by combining the mixed estimation based on two parameter estimation.Under the mean square error matrix criterion,it is proved that the new stochastic constrained two parameter estimation is superior to the mixed estimation,the two parameter estimation,the stochastic restricted ridge estimation and the stochastic restricted Liu estimation under the necessary and sufficient conditions,which are verified by the actual data and Monte Carlo simulation the new estimation has better parameter estimation effect.3.Based on the effectiveness of weighted mixed estimation and two parameter estimation in dealing with multicollinearity problem,a new weighted mixed two parameter estimation is proposed by combining two parameter estimation methods.Under the mean square error matrix criterion,the necessary and sufficient conditions for the weighted mixed two parameter estimation to be superior to the weighted mixed estimation and two parameter estimation are proved.Finally,the numerical simulation shows that the new estimation has better effect on parameter estimation.