Research Of Liu Estimator In Partially Linear Measurement Error Models

In epidemiology,analytical chemistry,drug testing,astrophysics and other fields,observational data containing measurement errors are often used to analyze models due to limitations such as measurement tools or manual sampling.If the measurement error is ignored,when the traditional statistical method is used to estimate the parameters of the regression model containing the measurement error,the estimated values of the parameters are usually inconsistent.At this time,the measurement error model is widely concerned.Linear regression model has always been the mainstream model of statistical research,but the model setting is too strong,and it is easy to lead to model setting error in practical application.The semi-parametric model,which combines the characteristics of parametric model and non-parametric model,comes into being.There are both linear and nonlinear parts in the model,making the model more flexible and more in line with the actual needs.The most common semi-parametric model is the partially linear regression model.When there are many variables in the regression model,the problem of multicollinearity is prone to occur in the model.At this point,the data matrix X’ X becomes almost irreversible and the variance of the least squares estimator becomes large and unstable.Biased estimation is one of the methods to overcome the problem of multicollinearity.The biased estimation method makes a trade off between the unbiased property of the estimator and the variance,and obtains a smaller mean squared error by sacrificing the unbiased property of the estimator.In this paper,a series of biased estimates are presented under partially linear measurement errors models.The parameter estimation method is studied when there is the problem of multicollinearity in the partially linear measurement error model,the Liu estimator of the partially linear measurement error model is proposed,the asymptotic properties of the Liu estimator are studied,and the Liu estimator is proved to be superior to the improved least squares estimator under the mean squared error criterion in the paper.The Monte carlo simulation results show that the Liu estimator is indeed more effective.Considering the prior information or additional information about parameters in the model is also an effective method to improve multicollinearity.This paper introduces the restricted Liu estimators under linear restrictions and random restrictions and further studies the properties of the restricted Liu estimators,making the comparisons between two kinds of restricted Liu estimators and the pure Liu estimator under the mean squared error matrix criterion.It is theoretically proved that the restricted Liu estimators of partially linear measurement error model perform better than the pure Liu estimator under certain conditions.Because the weights of the obtained sample information and restricted information of the parameters may be different,this paper proposes the weighted mixed Liu estimator of the partially linear measurement error model under the condition of random restrictions,studies the asymptotic property of the weighted mixed Liu estimator,and proves that it is better than the ordinary Liu estimator in the sense of matrix mean squared error.