Liu Estimation Of Partial Linear Variable Coefficient Models With Random Missing Response Variable

As long as it is related to the field of data research,the problem of missing data is common,so the study of missing data has always been the focus of statisticians.when fitting the model,we often assume that there is no Multicollinearity problem in the model.However,Multicollinearity is common in the actual data analysis,so it is inevitable to overcome the Multicollinearity problem in the model parameters in the regression analysis.On this basis,we consider the random loss of response variables and Multicollinearity problems in partial linear variable coefficient models.Firstly,an estimation method combining inverse probability weighted regression interpolation and Liu estimation is proposed.In this paper: the part of the data missing in response variables is temporarily "abandoned",and the remaining complete data set is used for regression analysis.In this process,the parameters and non-parameters of the model are estimated mainly by Profile least squares estimation;Secondly,the obtained model parameters and non-parameters are used to regression the data of the missing response variables to obtain the estimated interpolation values of the response variables.Different weights are assigned to the original and estimated response variables.Then,the "complete data set" obtained by weighted interpolation is used for regression analysis again to obtain the estimation of the new parameters and non-parameters of the model.Finally,the Liu estimator of the partial linear variable coefficient model is constructed when the response variables are missing and the linear part of the model has the Multicollinearity problem,and the asymptotic normality of the obtained estimator is proved.Secondly,this paper compares the performance of mean interpolation,mode interpolation and inverse probability-weighted regression interpolation under different missing probabilities through numerical simulation,and verifies the robustness of inverse probability-weighted regression interpolation.On this basis,numerical simulation is carried out again,considering the Multicollinearity of the parameter part of the model,the conclusions of numerical simulation I are applied to numerical simulation II.The Profile least squares estimate and Liu estimate are compared,and the advantages and robustness of Liu estimate are analyzed.Finally,the theoretical results and numerical simulation results are applied to the study of the Boston housing price data,and the effects of various data on the housing price are discussed.The empirical results show that the proposed method is practical and can be applied to the model fitting of Multicollinearity problems with random loss of response variables.